Viper users should cite papers from the following list appropriate to the features in the code they employed:
Sheard, G.J., Leweke, T., Thompson, M.C. & Hourigan, K. (2007) Flow around an impulsively arrested circular cylinder. Physics of Fluids 19(8), article number 083601.
Sheard, G.J. & Ryan, K. (2007) Pressuredriven flow past spheres moving in a circular tube. Journal of Fluid Mechanics 592, 233262.
Sheard, G.J., Fitzgerald, M.J. & Ryan, K. (2009) Cylinders with square cross section: Wake instabilities with incidence angle variation. Journal of Fluid Mechanics 630, 4369.
64bit (em64) OpenMP sharedmemory version: Optimized build: 15 May 2014
64bit (em64) MPI version (requires Open MPI 1.6.3 libraries): Optimized build: 31 July 2014
Windows (64bit): Optimized build: 15 May 2014  Bug diagnosis build: 15 May 2014
Windows (32bit): Optimized build: 15 May 2014  Bug diagnosis build: 15 May 2014
Viper Reference Manual (updated 15 May 2014)
The application get_period.exe can be used to determine the period (and hence the frequency) of a timevarying data set. Linux compiles of this code are available on request.
The code takes as input the following:
A text file containing a list of <tab> or <space>separated data. Each row must have the time in the first column, then any number (N) of subsequent data columns.
The data column number from which to calculate the period.
A reference value of the data at which to calculate the period.
The code works by finding and outputting the interpolated time between successive occasions where the data increases through the reference value. Thus to obtain the correct period/frequency you should choose a reference value which the data only increases through once per period. The code outputs the calculated periods to the screen, as well as a file named period_data.dat.
The code uses inverse cubic interpolation of the nearest four data points to the reference value to accurately determine the time at which the data equals the reference value.
Given an oscillatory signal representing the growth or decay of a solution to saturation, the application get_mode.exe can be used to estimate the mode amplitude A (as the envelope of the oscillation), and the quantities A^{2} and d logA/dt, which are required to determine the coefficients of the Landau model. The envelope of the oscillation is estimated over time by measuring the absolute values of the differences between successive maxima and minima. Linux compiles of this code are available on request.
The code takes input from text files containing columns of data, as with get_period.exe, and saves the calculated data to a default file mode_evolution.dat.
##################### # # # VIPER CHANGELOG # # # ##################### 31 JULY 2014:  Tzekih detected an "output statement overflows record" error during time stepping for the linearized Boussinesq NavierStokes solver used for linear stability analysis. This has been corrected by making the string used to store the text prior to displaying to screen. 16 APRIL 2014:  Added the spatial gradients of the scalar (temperature) field as allowable variables for the integrand expressions for the "int" and "intf" commands.  Added the spatial gradients of the scalar (temperature) field as allowable variables for the userdefined field variable (specified using the "u" option in the "tecp" command.  Added scalar gradients to the Tecplot output from SEFourier 3D simulations. 12 NOVEMBER 2013: *** Note: Tony has encountered crashing during SEFourier 3D MPI simulations (infrequently, and on the VLSCI system). This appears to be due to multiple processes attempting to simultaneously write to the output file. This has not yet been fixed ***  Fixed output from the "LINE" command, where "z" and "r" were being written to the output file header for Cartesian simulations, instead of "x" and "y". 4 NOVEMBER 2013:  Upgraded the "RAND" command to work for all flow fields (2D, 3D, linearised perturbation fields), in addition to the spectralelement Fourier 3D solver. 19 AUGUST 2013:  Found the error with Boussinesq computations. This was due to an incorrect scalar field (intermediate not endoftimestep) being used at a point in the time integration algorithm. This was especially damaging for simulations using cylindrical coordinates because there was a 1/r factor difference between the two fields. 16 AUGUST 2013:  In an attempt to track down the buoyancyrelated error that has crept into the code in the last few months, checking compilation of the code on different systems and with different compilers: 1) Using different versions of the Intel Fortran compiler on NCI Vayu and Raijin produces the same results for Kovaznay 2D flow test case. 2) Yet to check if buoyancy effects same on both compilations 3) Compiling the code on Vayu with GNU Fortran compiler found the following: a) Errors in "msg_passing" module if compiled as a nonMPI code b) Nonstandard use of .XOR. rather than .NEQV. for exclusiveor logical operations in the recent bandwidthminimisation experimental code in the messagepassing section of the code. 15 AUGUST 2013:  Detected a potentially serious error with the use of index mapping vectors of the form "indx_x_to_?", where statements of the form "f_x(:) = f_?(indx_x_to_u(:))" were not seeing the LHS being correctly filled with the content from the RHS. The same also applied to the "indx_el_to_?" arrays. This affected some 2D base flow derivatives, and several outputs, including the L2 norm. The L2 norm is now fixed, and all other affected areas have been replaced with more robust loops through all entries in the vectors. **** However, note that the Boussinesq buoyancy computations are currently incorrect ***** 6 AUGUST 2013:  Fixed an issue where the buoyancy coefficient may not be set to a default zero value if the user did not explicitly set a value when calling "buoyancy". 24 JUNE 2013:  Fixed a bug in the LOAD routine where interpolating a saved solution onto meshes with a different polynomial order was failing due to a vector already being allocated  this had crept in during the MPI upgrade.  Reverted to the behaviour where executing the LOAD routine changes the time step to that stored in the file. This is required as the file contains fields at the previous time steps, that would be incorrect if the time step is not set to be that in the saved file. 4 JUNE 2013:  Fixed a bug in the "line" command, which will now correctly output outofplane component of velocity and its derivatives if the wvelocity field is active in a 2D or axisymmetric simulation.  Fixed a bug with the "rotate" option recently added to the "tecp" command, where it was not correctly defaulting to a zero rotation angle if no rotation angle was specified. 3 JUNE 2013:  Changed "LOAD" routine behaviour  "dt" and "RKV" are no longer changed to values stored in the restart file, only "t" is taken from the file  the other parameters need to be set in the "viper.cfg" file.  Fixed an output bug in the "flux" commands where multiple MPI processes might each try to write to the same output file, despite only one thread doing the calculation. 30 MAY 2013:  Added a command "LINE", which extracts flow field data along a line from a 2D simulation. 24 MAY 2013:  Added an option "rotate" to the "tecp" command that rotates 2D or 3D hexahedral meshes clockwise by a specified angle in degrees about the origin in the Tecplot output files. This is useful for aligning visualized results with a specified gravity direction vector. 20 MAY 2013:  Fixed an error reporting bug that was incorrectly reporting errors about linearized perturbation field pointers not being associated when linearized perturbation fields were not being evolved in a 2D simulation. 7 MAY 2013:  Added spatial derivative routines capable of acting on the entire elementbyelement flow field vectors, "dd?_all_elem()". *** Note these did not give a detectable speedup and so have been replaced with the previous code. *** 6 MAY 2013:  Added a command "AVG_ONE_DIR", which takes a flow field and averages it along a specified direction. 5 MAY 2013:  Modified the "MASK" command so that it accepts separate mask functions for each velocity field component, as well as the scalar field variable. 29 APRIL 2013:  Fixed a bug in the new MPI_BCAST arrangement where an unallocated pointer storage was being accessed. The MPI_BCAST code segment should only be used when linearized perturbation fields are being evolved in addition to a base flow, but this was being executed when no linearized fields were being evolved accidentally. 8 APRIL 2013:  Changed the MPI_BCAST operation during evolution of linearized perturbation fields  now all velocity components are gathered together into a single broadcast of the base flow field to all processors, rather than calling multiple MPI_BCAST calls each time step. 3 APRIL 2013:  Completed the implementation of constant and linear forcing terms. This is implemented in 2D, 3D hexahedral and 2D linearized perturbation field solvers, including scalar fields. It is not yet implemented in SEFourier 3D simulations. 1 APRIL 2013:  Began the implementation of "gvar_forcing_fX" and "gvar_forcing_gX" commands used to implement constant and linear forcing terms in each velocity component momentum equation or the scalar advectiondiffusion equation. Here "X" may be "u", "v", "w" or scalar field "s". *** Have disabled commands that overlap with this forcing facility, including "pgrad", "quasi2d", "gvar_lorenz" *** Still need to implement in time integration > constant forcing: SEFourier 3D, > linear forcing: SEF 3D 11 DECEMBER 2012:  Ported Viper to MPI for parallelization. The MPI version, Vmpir, is not publicly available, but may be made available on request. Parallelization is employed both for SEFourier 3D simulations (tested beyond 1000 CPUs) and linear stability analysis evolving multiple linearized perturbation fields in parallel. 24 OCTOBER 2012:  Fixed a bug in the advection for scalar fields in Cartesian coordinates relating to an incorrect spatial derivative term. 17 OCTOBER 2012:  Fixed an incorrect vector size allocation issue for the Arnoldi solver for linear stability analysis and transient growth analysis that had emerged since the recent alteration to the numbering of velocity components. This bug only presented itself when different boundary conditions were imposed on each of the velocity components. 20 SEPTEMBER 2012:  Fixed a divergence error in the evolution of linearized scalar fields for linear stability analysis in cylindrical coordinates  I had forgotten to premultiply the intermediate velocity field after the advection substep by the radial coordinate.  A segmentation fault in linearized evolution of perturbation fields in cylindrical coordinates with nonzero swirl (wvelocity) was traced to a requirement that WVEL be placed before PERT. 17 JULY 2012:  Updated the code used to advect scalar perturbation fields. Previously the advection routines were incorrect/unimplemented for linear stability analysis with scalar fields active.  Moved routines around in source code package. Previously most linear perturbation field routines and scalar field routines were in "floquet.f90" and "scalar.f90". Now advection, pressure and diffusion routines for base, perturbation and scalar fields are grouped in "ti_advect.f90", "ti_pressure.f90" and "ti_difusion.f90". This is intended to improve the logic and readability of the source code package. 17 JUNE 2012:  ########################################################################### # # # Initiating a MAJOR change behind the scenes in Viper's code base. This # # will facilitate the ability to SEPARATELY specify Dirichlet OR Neumann # # boundary conditions for the individual u, v, & w components of # # velocity. This requires new mapping arrays to be built for each # # component, and separate Helmholtz matrices to be constructed for the # # diffusion solves for each component. New "btag" variables "u", "v" and # # "w" can now be specified instead of the combined "vel" specifier, # # though the legacy "vel" specifier will be retained for backwards # # compatibility. Users should compare results using new versions of Viper # # with their previous versions to ensure that nothing has been broken # # by this upgrade. # # # ########################################################################### 18 MAY 2012:  Fixed a bug in the 'int' command where an unassociated scalar field array was being addressed in spectralelement/Fourier 3D computations which did not feature a scalar field. 11 MAY 2012:  Found another bug in the 2D Boussinesq solver that crept in when the "iterate" command was implemented  this one was seeing the buoyancy correction use potentially the incorrect temperature field vector for the buoyancy term.  Found a bug whereby a mask used to identify nodes lying on the axis (with global velocity numbering) could be corrupted in some scalar field simulations conducted in cylindrical coordinates, depending on the boundary definitions. This has now been fixed. 10 MAY 2012:  Fixed a possible error that emerged when "bouss" was called in an axisymmetric simulation, where a stressfree boundary intersected the symmetry axis. In this situation, it was possible that the inexact stressfree boundary correction could lead to a nonzero radial velocity on the corner node of an element sharing the symmetry axis and stressfree boundaries. This was leading to contamination of the velocity field, first across the symmetry axis, and then throughout the flow. Now, at the end of the symmetry boundary correction, the code explicitly sets the vvelocity to zero along the symmetry axis. 2 MAY 2012:  Changed the behaviour of "gvar_dt", "gvar_RKV" and "gvar_scalar_diff" in the "viper.cfg" file  they now accept functions of userdefined variables, so "gvar_usrvar" functions/variables may be created prior to defining those parameters, and the parameters can then be expressed in terms of those user defined quantities.  Changed the functionality of the "bouss" command to permit separate specification of the sign of the required buoyancy (the first coefficient) and the magnitude of the buoyancy coefficient. The command now also accepts the buoyancy coefficient as a function (including userspecified variables). 17 APRIL 2012:  Added a DEBUG command, which can be called to write more info to screen during program execution for bughunting purposes. Note that additional output will not be large, and will change over time as new features are added into the code.  Added the capacity for iteration of 2D base flow fields to see if rates of temporal convergence could be improved for Boussinesq simulations. This is invoked using the new command ITERATE. 14 DECEMBER 2011:  Added a new command "moments" which calculates the moment on a boundary in 2D simulations. 27 OCTOBER 2011:  Further minor code tweaks to several routines to correct warning messages from "gfortran" compiler. 26 OCTOBER 2011:  In a behindthe scenes alteration, some source code has been restructured to replace Intel Fortranspecific syntax with standard Fortran code, making it easeir to compile Viper on nonFortran systems. 13 JULY 2011:  Fixed the bug in the "TRACK TECP" binary output routine (I hope!).  A bug in the "TRACK TECP" binary output routine was detected. Currently this feature doesn't work  use "ascii" option. 9 JULY 2011:  Added a new function, "track load" to load binary restart files for particle transport simulations that are created using the new "track save" function.  Changed the operation of "track save". It now outputs a binary restart file for particle transport. 8 JULY 2011:  Added a new function "track tecp" to output particle data in binary or ASCII Tecplot point data file formats.  Changed the "track save" functionality (ASCII output of particle locations) to "track saveold"  this is to facilitate the upcoming particle transport restart (save/load) functionality. 6 JUNE 2011:  Added the gradients of the scalar field to the "vars ddx" output option of the "tecp" command. This is implemented for all 2D solutions and 3D hexahedral solutions. 11 APRIL 2011:  Fixed a bug in the math parser routine, where the function simplifier code was returning functions with two negative signs next to each other when it pre evaluated an addition/subtraction of two constants appearing after a negative sign, that returned a negative number as the result of the evaluation. e.g. 'x  3  5' was becoming 'x2' rather than realizing that a "3" is being added to a "5". 4 APRIL 2011:  Fixed a bug in the math parser routine, where the function "rand" was being incorrectly preevaluated by the function simplification code. 13 JANUARY 2011:  Found a bug that slightly corrupts the SEFourier 3D solver when a scalar field and Boussinesq computation are being carried out. This related to incorrectly mapping the differently numbered velocity and scalar fields during advection calculations. 5 JANUARY 2011:  Modified LOAD behaviour: If called before INIT, the "viper.cfg" Dirichlet boundary conditions are applied, overwriting whatever was on those boundaries in the restart file. If, however, the user calls LOAD after INIT, then static Dirichlet boundaries remain as whatever they were in the file, rather than what is in the "viper.cfg" file. 20 DECEMBER 2010:  Added scalar field to SEFourier 3D versions of "int" and "flux" routines. 16 DECEMBER 2010:  Added an option "hugh" to the "save" command to output 2D or perturbation field data to an ASCII file readable by SEMTEX, Hugh Blackburn's spectral element code. 13 DECEMBER 2010:  Added Boussinesq modeling capability to SEFourier 3D solver. 11 DECEMBER 2010:  Problem solved: turned out to be a boundary condition mismatch.  Tested the "AXIROTATE" command in both the base flow and linear stability analysis solver  something not working in perturbation field solver  investigating. 10 DECEMBER 2010:  Added the "AXIROTATE" functionality to the cylindricalcoordinate formulation of the spectral elementFourier 3D solver.  Added a command "AXIROTATE", which allows 2D computations conducted in the cylindrical coordinate system (with "AXI" activated) to be computed in a rotating reference frame. 30 OCTOBER 2010:  Added a command "INTF", which works like "INT", except it outputs integrals evaluated on each mode of a spectral elementFourier 3D computation, and the results are output similar to the "ENERGYF" command. Note that the integrand is calculated using the magnitude of the complex Fourier coefficients at each mode. e.g. This command could be used to generate output akin to ENERGYF, but with a conditional mask so that the energy is only integrated over part of the domain (say, radial values less than 2 units in cylindrical coordinates). The usage in this case would be: \> intf u 'if(y<2,u^2+v^2+w^2,0)'  Added an option "nozero" to the Tecplot output routine "tecp", which removes the fundamental mode (zerowavenumber component) from spectral elementFourier 3D data when creating a Tecplot output file. This is especially useful for isolating 3D/nonaxisymmetric flow structures from swirling flows in cylindrical coordinates, for example. 16 SEPTEMBER 2010:  Modified behaviour of LOAD routine so that static Dirichlet BCs are overwritten by what is in restart file rather than what is specified in "viper.cfg", provided LOAD is called AFTER "init". 2 September 2010:  Windows builds are now available for both IA32 and Intel 64bit architectures. 28 JULY 2010:  Added the capability for the SVD driver to optimize energy norms containing only a selection of the available velocity component / scalar field, rather than all of them (i.e. norm E = u^2+v^2+w^2, plus s^2 if active), which is the default behaviour. 15 JULY 2010:  Added the capability for GETMINMAX and SAMPLE to be employed on perturbation fields. 7 MAY 2010:  Altered the Tecplot output of SEFourier 3D data in cylindrical coordinates so that if the data set represented a complete revolution in the azimuthal direction, the data set would be continuous through the interface between 2*pi and 0 degrees (this eliminates the appearance of a boundary plane visible in the data). 5 MAY 2010:  Added the ability for the default SAVE and LOAD routines to interpolate onto different meshes (using the m option, just as with the old SAVE/LOAD functionality). To use, first the "m" option must be added when saving a solution, and then to interpolate onto a different mesh, include the "m" option when calling LOAD in a new simulation. 1 MAY 2010:  Added diffusion to 2D and 3D hexahedral particle transport algorithms, by way of a Gaussiandistributed random walk. The user specifies the Schmidt number using the new "TRACK DIFF" command. 1 APRIL 2010:  Parallelized calculation of "track sample" output from SEFourier 3D particle tracking computations, and now carrying out file output of particle data only once per time step to hopefully improve the speed of this process. 29 MARCH 2010:  Fixed an error in a formatting statement for output from "TRACK SAMPLE" in SEFourier 3D simulations.  Added the scalar field to MONITOR output from SEFourier 3D computations. 21 MARCH 2010:  An unallocated scalar numbering index was being incorrectly referenced in simulations in which the scalar field was inactive, leading to a segmentation fault. This has been fixed. 20 MARCH 2010:  Added scalar field to Tecplot output from SEFourier 3D computations.  Added treatment of scalar fields from SEFourier 3D jobs to save & load routines. 19 MARCH 2010:  The option of adding a scalar field to the SEFourier 3D algorithm has been added to the code's functionality.  The particle tracking "track save" routine has been rewritten for SEFourier 3D computations  now instead of calculating data, opening, writing and closing the output file for every particle (which can be many), the code now only opens and closes the file once  all calculation and output is conducted while the file is open. Have also removed the redundant transformations from parametric to physical space and back again. These alterations should make the "track save" command faster. 5 MARCH 2010:  Added scalar field its spatial derivatives to output from 2D/3D calls to "SAMPLE". 6 FEBRUARY 2010:  Changed the norm being optimized using the SVD transient growth solver to "u^2+v^2+w^2+s^2" when a scalar field is active. Previously, a standard kinetic energy norm of "u^2+v^2+w^2" was implemented. 12 JANUARY 2010:  Altered behaviour of RAND for SEFourier 3D computations. By default, less randomization is applied to higher wavenumbers. However, this behaviour was also being applied even when the user was discretely randomizing a single mode (using the "k" option in RAND). This behaviour has been corrected  now when the "k" option is used, the specified level of randomization will be applied to whichever mode is specified. 6 JANUARY 2010:  Altered output from "energyf" command so that the fundamental mode was listed as mode 0, and corrected the behaviour of "rand", so that spanwise/azimuthal Fourier modes were randomized from number 0, not 1, when using the "k" option. 21 DECEMBER 2009:  Improved the streamfunction output in Tecplot: now a Stokes streamfunction field is plotted from axisymmetric computations (thus the streamfunction contours align with streamlines for computations in both Cartesian and cylindrical coordinates. 18 DECEMBER 2009:  Found an incorrect derivative term in the advection step of the linearized NavierStokes solver in Cartesian coordinates with an outofplane (w) component of velocity active in the base flow. 15 DECEMBER 2009:  Fixed an error with particle tracking in cylindrical coordinates, in which an interpolation error in the azimuthal component of velocity caused particle trajectories to oscillate within elements touching the axis of symmetry. 1 DECEMBER 2009:  Added the "psi" (streamfunction) variable to the Tecplot output routine. This allows a streamfunction field to be calculated and output in a 2D simulation without an outofplane velocity component. 27 NOVEMBER 2009:  Removed diagnostic output from SVD computation as testing has shown it to be working. This speeds up the algorithm.  Corrected a pointer initialization affecting initialization of simulations of a scalar perturbation field on some platforms. 25 NOVEMBER 2009:  Modified the Arnoldi solver so that if a user initiates an Arnoldi solve from a restart file from a previously converged run, then the solver will recompute and ouput eigenvalues/eigenvectors from that run (this capability allows Tecplot or Viper restart files to be regenerated from an Arnoldi restart file, or when using the SVD solver, it will allow multiple transient growth calculations from a single set of computed eigenmodes.  Fixed an eigenvalue normalization issue affecting the SVD driver routine  this now appears to work  for cases with and without a scalar field, this routine seeks to find the transient growth based on maximisation of a kinetic energy norm. 15 NOVEMBER 2009:  Two significant capabilities have been incorporated into the LOAD routine: (1) A new option "r" has been added which allows a user to add the stored flow field in a restart file to the present computation, rather than the default behaviour of overwriting the existing fields. (2) A new option "a" can be used to specify a scaling factor for the field being loaded. 8 NOVEMBER 2009:  Replaced two MAT_MUL functions in the static condensation evaluation routines with BLAS "dgemv" routines  this has resulted in a small speedup (approx. 5%) in some cases. 6 NOVEMBER 2009:  Now normalising ouput flow field from SVD transient growth routine to unit energy.  Streamlined the time step timing statistics output further.  Improved output during Arnoldi iterations  the code now provides more information about how many cycles remain in each Arnoldi iteration. 4 NOVEMBER 2009:  Fixed an error in the output of timing stats for sparse solves in parallel computations.  Modified the QUASI2D command to allow the friction coefficient to be supplied as a function. 3 NOVEMBER 2009:  Altered appearance of "max du" monitors during time stepping. 2 NOVEMBER 2009:  Added file format checking to Arnoldi restart files. Viper will now report an error and abort an Arnoldi call if an existing restart file is incompatible (this follows the 25 October 2009 update to the Arnoldi solver). 31 OCTOBER 2009:  Improved spatial derivative timing test so that more accurate timings are calculated when parallel jobs are executed. 30 OCTOBER 2009:  Fixed the perturbation field time step routine so that zerowavenumber fields can be computed in axisymmetric computations with swirl. 27 OCTOBER 2009:  Tweaked text output in LSA and TG driver routines. 25 OCTOBER 2009:  Changed the format of vectors passed to the Arnoldi solver. *** Note that this modification makes new Arnoldi restart files incompatible with the previous format. *** Only the homogeneous node values are passed to the solver, rather than the full velocity vectors  the zero Dirichlet nodes have been omitted to reduce the size of the Arnoldi matrix problem. Also, the real and imaginary components of the perturbation field vectors are all sent to Arnoldi as entries of a real vector (as a complex vector sent to Arnoldi implies a temporal representation, whereas complex perturbation field vectors imply a spanwise spatial representation). 20 OCTOBER 2009:  Corrected a flaw in the LOAD routine. It was incorrectly giving an error if a user tried to map a field onto a Fourier mode in an SE/Fourier 3D simulation. 15 OCTOBER 2009:  Removed a superfluous blank line written to screen at the conclusion of the SAVE command. SAVE output should now more closely resemble TECP output. 12 OCTOBER 2009:  Chris Butler detected an aliasing artefact in vorticity which arose in postprocessing for Tecplot output from SE/Fourier 3D computations. This was traced to incorrect indexing of conjugate (ve frequency) modes when vorticity fields were reconstructed from Fourier modes. 11 OCTOBER 2009:  Added driver commands for both linear stability (Floquet) analysis and transient growth analysis. These are named "LSA" and "TG", respectively. These single commands can be used in place of a loop containing ARNOLDI and STEP commands. 8 OCTOBER 2009:  An error with one advection term in the adjoint solver for transient growth analysis was uncovered after testing code against Hugh Blackburn's SemTeX code. This has now been fixed. 1 OCTOBER 2009:  Added additional error messages to the PARDISO sparse matrix solver error reporting routine to conform to the Intel MKL 10.xxx implementations. 30 SEPTEMBER 2009:  Added error messages to the LOAD command: If a user specifies a nonzero perturbation field number ("k" option) before FLOQ has been called, an error message is reported and the LOAD routine terminates. If a larger perturbation field number is supplied than what is active, a warning is printed to screen, and the fields are loaded onto the largest active field number.  Joine identified a problem with stability analysis of frozen base flows with the ROTATE command active. It was identified that the rotating component of the base flow was not being subtracted in spatial derivatives of the base flow (this arose from a change to the code on 8 September). 27 SEPTEMBER 2009:  Slightly modified the names given to output from the Arnoldi command to more closely resemble default output from SAVE and TECP, and to remove association with Floquet analysis, as ARNOLDI is also used for transient growth. 26 SEPTEMBER 2009:  Added timing output during time stepping in transient growth calculations.  Added code to the time integration routine for perturbation fields which is designed to minimise the error in the first couple of time steps due to the unavailability of the full number of velocity fields from previous time steps. This is achieved by reducing the order of extrapolations from previous flow fields so that only available fields are used. i.e., if the time integration order is 3rdorder, then for the first step a 1storder scheme is used, and for the second step a secondorder scheme is used. Thereafter, the 3rdorder scheme is used as normal. 23 SEPTEMBER 2009:  The "max du" monitor in the SE/Fourier code was being incorrectly calculated thanks to misplaced brackets. This has been rectified. 22 SEPTEMBER 2009:  Fixed a problem with 3D hexahedral particle tracking  some particles were occasionally misplaced during element interface traverses.  In the particle tracking routien, added a CLOSE statement to release the injector coordinate file "track_pts" immediately after the points have been read.  Changed the misleading reference to "Element order N = ..." during startup to "Element polynomial degree N = ...". The element order is technically N1.  Repaired a recently arisen pointer access violation causing the 3D hexahedral solver to crash during the INIT call. No time integration algorithms were affected. 18 SEPTEMBER 2009:  Added a runtime check of the speed of three alternatives for computing spatial derivatives: sparse matrixvector product, full matrixvector product, and tensorproduct construction (summed from derivatives in each elemental parametric coordinate direction). The fastest method is determined at runtime, and is used for that simulation. The sparse matrixvector product approach was used previously, but the other methods can be significantly faster, depending on the element polynomial degree used, etc. Users may notice decent speedups, particularly in the advection term, and to a lesser extent in the pressure term, which are spatialderivativeevaluations intensive. 9 SEPTEMBER 2009:  Followed up on an issue reported by Chris Butler  the Intel Fortran compilers (ver 11) issue an internal compiler error when they encounter an "OMP ATOMIC" statement in a subroutine which may or may not be in a parallel region of code. Temporarily removing these calls (they are not solutionsensitive as they are only used for timing statistics).  Attempting an explicit initialization of the elemental Laplacian matrices to zero at the beginning of its construction to see if this avoids the NaNs appearing in the matrix when it is build using the Intel MKL 10.1 libraries on the EM64 xe.nci.org.au machine. 8 SEPTEMBER 2009:  Stability analysis of multiple wavenumbers now skip fields which have converged, permitting runs to speed up as modes converge. Note that to exploit this speedup, multiple modes will have to be computed on each parallel thread.  Shifted computation of base flow spatial gradients from within base flow and perturbation field advection calculation routines to a single evaluation at the beginning of each time step. This will permit faster time integration in stability analysis computations. Speedup tests have shown improvements of approximately 10%. 7 SEPTEMBER 2009:  Added an extra optional parameter to the ARNOLDI command which allows the user to specify the exponent of the convergence tolerance (the default is 7, i.e. 1e7). Numbers with smaller magnitude (e.g. 5, 4, 2, etc.) will converge faster, but with less precision. 6 SEPTEMBER 2009:  Fixed an issue with the solver for zerowavenumber perturbation fields in cylindrical coordinates, which should allow the zeroth wavenumber (axisymmetric) mode to be evolved stably. 5 SEPTEMBER 2009:  Added checking for infinities as well as NaN values when monitoring for divergence of the solution due to instability in time integration. 2 SEPTEMBER 2009:  The Womersley profile feature has been implemented in both the 2D and SE/Fourier algorithms (AXI should be used in both cases). 1 SEPTEMBER 2009:  Added a feature to WOMERSLEY command which allows the profile to be constructed given areaaveraged velocity Fourier coefficients instead of pressure gradient coefficients.  Added a command WOMERSLEY which can be used to impose a Womersley velocity profile based on supplied Fourier coefficients of an imposed timedependent pressure gradient.  Added an error report which picks up when a usersupplied function has imbalanced brackets. 24 AUGUST 2009:  When loading from stored flow fields and changing the time step, this causes the fields at the two stored previous times to be incorrect. A routine has been added to the "SET DT" command to interpolate these previous fields to the correct times. Theoretically, this should provide for a smoother restart for runs where the time step is abruptly changed. 22 AUGUST 2009:  Internal code change: On IA64 systems (such as APAC), the 2D time integration routine was not being optimized during compilation due to its large size. This has now been restructured, with parts of the routine being split off into separate subroutines, and compilation is again optimized. Users may notice a speedup for 2D simulations on APAC.  Internal code change: Previously was using a condition "Nfloq_modes>0" to check if perturbation fields were active. This has been replaced by a LOGICAL condition "isFloq", which is quicker to evaluate and cleaner in the source code.  Time integration now includes trapping of divergence due to time integration instability. Viper will immediately terminate if divergence is detected. Divergence is considered to have occurred if "NaN" is present in any of the flow field vectors. 16 AUGUST 2009:  Added the capability for RECONSTORE to store spanwiseaveraged snapshots from SE/Fourier 3D computations (previously only storage of 2D quadrilateral or 3D hexahedral solution data was facilitated). This will enable stability analysis of the 2D field corresponding to a spanwise average of a spanwiseperiodic 3D solution to be carried out (note that the spanwiseaverage is simply the fundamental mode of the spanwise Fourier modes of the flow field). 14 AUGUST 2009:  Added evaluation of the present time base field when starting transient growth calculations from a reconstructed base flow. This may have been leading to a slightly inaccurate startup of the perturbation field. 11 AUGUST 2009:  Added evaluation of the base flow velocity field at two previous times at the beginning of transient growth computations in which the base flow is being reconstructed (to ensure that the guess of the futuretime base flow used in advection of the perturbation fields is correct). This is also done to acquire the two futuretime fields for the adjoint (backwardstime) solve in transient growth analysis.  Further speedups to RECONLOAD: The pressure field is now not computed by default, as it is not needed for stability analysis. Users can choose to compute this using the "p" option in RECONLOAD. Speedups for Fourier, polynomial and Akimabased reconstructions were 21%, 28% and 27%, respectively, for the test case used for the 10 August 2009 tests. 10 AUGUST 2009:  Added quasi2D friction term to perturbation fields for linear stability analysis: as with the base flow, this term is activated if the command QUASI2D is called. It should only be used in 2D Cartesian simulations, and the stability analysis will only be meaningful if the zeroth (2D) spanwise wavenumber is analysed (i.e. calling FLOQ 0).  Added BLAS "daxpy" calls for vectorscalar product & sum operations in polynomial interpolation routine using RECONLOAD. In a test case, a speedup from 4.8 to 4.0 seconds was achieved (17% improvement).  Added BLAS operations to substantially speed up the Fourier reconstruction code using RECONLOAD  a test case improved execution time from 31.9 seconds to 2.15 seconds (93% improvement).  An error was found in the advection term for perturbation fields in cylindrical coordinates with a nonzero wvelocity in the base flow (e.g. Stuart Cogan's swirling flow in a cylindrical vessel driven by a rotating base). This was introduced with the June/July transient growth upgrade, and has now been fixed. Tests with a 4 May 2009 build of the code verified (a) that the Cartesian and regular axisymmetric solver was unaffected (both for base flows and perturbation fields), and (b) that there was no difference between predicted stability modes using either STAB or ARNOLDI. 9 AUGUST 2009:  Found a LAPACK work array which was not being properly deallocated before a new allocation call  this affected ARNOLDI calls with WVEL active only.  Achieved substantial speedups to polynomial and Akima reconstruction of velocity fields using RECONLOAD. A test case had 25 elements of order 7, and 20k steps took 50 seconds to time integrate. Polynomial interpolation sped up from 77.8 to 4.70 seconds, and Akima interpolation sped up from 36.7 to 4.61 seconds. 8 AUGUST 2009:  Added Akima spline interpolation to the flow field reconstruction schemes available through RECONLOAD  this should be used in place of polynomial interpolation to avoid wiggle artifacts. 6 AUGUST 2009:  Fixed an array reference bug in RECONLOAD  the pressure field was being reconstructed incorrectly, which sometimes led to unexpected crashes due to an incorrect array being referenced. 5 AUGUST 2009:  Fixed a bug in Cartesian scalar transport  the 30 July fix to the cylindrical scalar transport algorithm broke the Cartesian solver. Now both are fixed.  Adjusted output of TRACK SAMPLE commands so that the report to the user that data is being written is only performed once per call, not once for each particle. 3 AUGUST 2009:  Added to the output of the FLUX command the integrated absolute value of the flux in addition to the integrated flux along each boundary. 2 AUGUST 2009:  Improved ARNOLDI command  now works for multiple perturbation fields. 31 JULY 2009:  Repaired scalar field timer for 3D hexahedral simulations (it was not being calculated), and restructured timers so that the time to evaluate the scalar field would be counted for both reconstructed as well as integrated flows. 30 JULY 2009:  Added the potential to use polynomial interpolation as an alternative to Fourier interpolation when using RECONSTORE and RECONLOAD (formerly FOURIERSTORE and FOURIERLOAD).  The previously unused cylindrical formulation of scalar advectiondiffusion contained an error which has now been rectified.  Identified that the code used to eliminate duplicate interpolated nodes in the Tecplot output routine was particularly slow in larger 3D hexahedral jobs  attempts are underway to speed this up.  Corrected output of "max ds" for scalar field computations in 3D hexahedral simulations  it now adheres to the minimum 1second between outputs. 22 JULY 2009:  Altered how output is displayed during time stepping. Now the step/time/max_du information is written at most once per second (thus not every time step is displayed). This will produce smaller output files, and will reduce the amount of I/O performed by the code  this should be helpful on queued systems such as SunGrid, APAC, etc.  Changed the computation of the change in velocity and scalar field monitors during time stepping. Now, instead of outputting the maximum change in the magnitude of velocity in the flow, the monitor now displays the maximum change in any one of the velocity components (u, v, w). This should very slightly speed this calculation up, and will also avoid over or underflow of the calculated quantity. 21 JULY 2009:  An error in the Tecplot routine for SEFourier simulations was incorrectly rendering the pressure field  an alternative approach has been taken for reconstruction from the Fourier modes.  An incorrect divisor was used in a MOD() function in the cylindrical formulation of the SEFourier code. This was causing incorrect radius values to be employed when computing the advection terms.  To aid in bug diagnosis, all versions of the code are currently compiled with the "traceback" option set, which will report routine/line number information where an error might have occurred in the source code. Let Greg know if this noticably slows things down.  Joine detected an error occurring during LOAD which was tripped by interpolation to a different element polynomial order under the optimized "em64" build of the code. This has been fixed by preallocating the pointer array causing the problem. 20 JULY 2009:  Fixed bug where a logical vector "radial_mask" was causing the code to crash in some 2D runs on Windows due to it not being allocated.  ARNOLDI now uses the new restart file format (consistent with the standard SAVE and LOAD calls). Also, the extracted eigenvector fields are copied onto the fields at previous times to avoid an unexpected kick being added to a simulation upon restarting. 16 JULY 2009:  Changed the functionality of L2 and INT commands. They now take their parameters as options, and have the added capability of being used to evaluate integral norms on perturbation fields was well as base flow fields. Note also that the L_2 norm is now computed as the square of the velocity magnitude, i.e. u^2 = u^2 + v^2 + w^2. 11 JULY 2009:  Fixed a problem with the routine used to return the parametric coordinates within an element corresponding to a physical coordinate. This issue meant that on some occasions during particle tracking or returning values at a point (using SAMPLE), the coordinates were returned before the solution had fully converged. Note that the worstcase scenario would be that the returned point could be between the desired point and the nearest mesh node. 8 JULY 2009:  Tweaked the allocation of storage for the Fourier reconstruction of velocity fields. The facility now will use less memory, and may be a tiny bit quicker.  Fixed an error in the routine used to compute strain rate at a point in the flow using either "SAMPLE" or "TRACK SAMPLE" in SEFourier computations in cylindrical coordinates  the returned strain rate may have been miscalculated at the axis. 1 JULY 2009:  Applied an indexing refinement to the FOURIERLOAD routine, which achieved a slight speedup. 30 JUNE 2009:  Implemented new commands (FOURIERSTORE and FOURIERLOAD) which can be used to save a timevarying solution of a two or threedimensional base flow as a Fourier time series, which can be used in a subsequent simulation to supply a periodic base flow for stability analysis computations, for instance.  Deleted some redundant code used to supply the radial distance in the global velocity numbering sense for computations in cylindrical coordinates. 23 JUNE 2009:  The 2nd term in the advection operator for the adjoint operation in transient growth computations was incorrect. This has been rectified. 19 JUNE 2009:  Added the capability of a scalar perturbation field to be used with ARNOLDI for stability analysis.  Added the ability for the SAVE and LOAD routines to recognise scalar perturbation fields.  Scalar perturbation fields should now be plotted in Tecplot files using TECP.  Cleaned out some unneccesary matrix storage for base and perturbation scalar fields. 18 JUNE 2009:  Added a scalar perturbation field for stability analysis, plus a Boussinesq term in the perturbation field time stepping routine. This will facilitate stability analysis of Boussinesq flows, and is activated by activating a scalar field and calling BOUSS as well as FLOQ.  Modified the function simplifier to do a better job of trimming zeroes off numbers. 15 JUNE 2009:  Added the capability to compute linear stability analysis of perturbation fields with zero wavenumber. 12 JUNE 2009:  Implemented a trial algorithm for transient growth calculations of frozen base flows.  Fixed an allocationrelated crash affecting Cartesian stability analysis jobs. 10 JUNE 2009:  Fixed a minor bug in which scalar transport fields were receiving an undesired perturbation upon restarting from a saved file. 5 JUNE 2009:  Reintroduced a little more output in the LOAD routine  in particular, the routine now reports if any parameter values are changed while reading from the restart file, and also reports on mismatches in resolution requiring reinterpolation. 3 JUNE 2009:  Fixed a bug in the function simplification routine  functions which when simplified occupied a longer string were being accidentally truncated.  Fixed a bug in LOAD where complex perturbation fields from stability analysis were not being mapped onto nonzero Fourier modes of an SEFourier 3D simulation correctly. 2 JUNE 2009:  Detected a 2nd error with the LOAD routine in terms of mapping 2D fields onto SEFourier modes  all fields were being zeroed out each call to LOAD. 1 JUNE 2009:  Detected an error in the LOAD routine caused by today's earlier fix, which could cause parameters to be loaded incorrectly. This has now been corrected.  Added some further minor streamlining to the function simplification routine. Routine should now be a little less memory hungry.  Fixed a bug in the LOAD routine which will now allow multiple 2D field to be mapped onto SEFourier modes using the "k" option. 31 MAY 2009:  Implemented some memorysaving and timesaving changes to the function simplification routine. 29 MAY 2009:  Made the output of the SAVE and LOAD routines more compact. 28 MAY 2009:  Restructured the LOAD routine for faster performance. Storage size is determined by making a pass of the file, avoiding excessive reallocation and copy operations.  An error was identified in the SEFourier algorithm  the symmetry boundary correction was accidentally placed outside the loop through the number of planes, causing the "k" index to the plane number to be undefined, resulting in an outofbounds error.  Replaced some conditional evaluations (e.g. "IF (Ninner > 0) THEN...") with a preevaluated LOGICAL parameter (e.g. "IF (isNinner) THEN..."). 27 MAY 2009:  Stripped out nonNewtonian code and compressible flow code, which were unused, untested, or not implemented. 25 MAY 2009:  Added a timer for the scalar field in time stepping. 22 MAY 2009:  Implemented a new command, ORDER, which can be used to change the order of the time integration scheme used for velocity or scalar fields. Allowable integration orders from 1 to 3 are facilitated. 21 MAY 2009:  Identified that a use of the FORTRAN function MINLOC to determine the element and node numbers of a global number (used in boundary condition, initial field, Boussinesq updates, etc.) was extremely inefficient. These have been replaced by preevaluated indexing vectors.  Implemented a command "FLUX", which outputs the flux of a scalar field through each boundary. 20 MAY 2009:  Fixed a bug in which scalar fields were not being properly loaded from restart files.  Slightly restructured the parallelization applied to the advection substep of the SEFourier 3D code. Small speedups (1% to 5%) were observed in testing.  Replaced some "divide by radial distance" operations with multiplication by a preevaluated 1/R quantity for efficiency. 19 MAY 2009:  Fixed a rare allocation error affecting 2D simulations in which there were more curved boundary filaments than there were numbered boundaries. Storage is now fully dynamic in the 2D curvature construction algorithm. 14 MAY 2009:  Improved the code used to print numbers to screen in a neat readable format. Now trailing zeroes are removed for numbers in scientific notation as well as decimal notation.  Improved the function simplification algorithm. Functions of constants (e.g. "cos(45.23)" are now also preevaluated (trigonometric, exponential, log, absolute value and square root functions are facilitated. This can make userdefined functions smaller, and may result in a slightly shorter evaluation (hence compute) time.  Fixed a bug in "gvar_movref"  if 3 functions were not explicitly supplied, the function simplification routine broke down attempting to process a null string. 12 MAY 2009:  Modified the functionality of STOPCRIT  now the current loop iteration that is being executed when the STOPCRIT threshold is breached is completed, and no further loop iterations are entered.  Added a safeguard to avoid the endless output encountered when a "viper.cfg" file contains an "mesh_file" statement pointing to a file which doesn't exist. Now Viper will only prompt for a filename 3 times before terminating.  Streamlined the SEFourier 3D algorithm: Only the positive frequency spectrum is stored in the velocity field vectors, reducing the memory footprint of the code. Also, all forward & backward transforms now computed at the higher resolution employed for advection (either 50% extra modes or 1 extra mode, if the "alias" option is employed in FOURIER or not, respectively). Thus the Tecplot output will be interpolated onto a slightly higher number of planes by default. These improvements to the SEF algorithm mean it is no longer necessary to perform tweaks to maintain stability  the pressure correction is now again enforced on all nonzero Fourier modes, and it is not necessary to explicitly enforce the fundamental mode (or the highest mode when the number of planes is even) to be real only. 8 MAY 2009:  As part of the improvements to the SEFourier treatment of Fourier modes and aliasing (i.e. all BCs and advection evaluated at higher Fourier resolution, and only lowest Mfourier_planes/2 nonzero modes being retained in the computations), the imposition of symmetry boundary conditions has been reverted to Fourier space (this was switched to real space in a recent attempt to hunt down the problem affecting Stuart Cogan's simulations, which in fact was caused by the incorrect order of the diffusion part of the highorder pressure BC). 4 MAY 2009:  Chris Butler reported some curious phenomena when complicated boundary conditions were imposed on 3D spectralelement/Fourier simulations  namely, if the boundary condition energized all Fourier modes in the discretization, then the solution was displaying degraded convergence, and the highest pressure mode was sometimes being contaminated with spurious artifacts. These effects were dependent on the relationship between the symmetry of the boundary conditions and the number of planes being selected. These problems were partially alleviated by switching off the pressure update of the highest Fourier mode in the computation (effectively relaxing the discretization of the pressure term). The contamination in the fundamental mode near the axis when an odd number of planes was used was found to be due to an insufficient Fourier resolution  care must be taken to ensure that sufficient Fourier planes are employed to fully resolve the boundary conditions as well as the interior flow. 1 MAY 2009:  Joine So reported a bug in GETMINMAX which was causing the code to abruptly crash. This was traced to a "log10" function that was sometimes being supplied a negative argument. This has been fixed. 22 APRIL 2009:  Added an option "k" (which can replace the "n" option) to the FOURIER command. This allows the user to directly specify the number of Fourier modes they require in an SE/Fourier 3D computation  this will make parallel computations easier to set up, as the number of modes must be an integer multiple of the number of available threads for maximum efficiency.  Added an option "alias" to the FOURIER command, which can be used to specify if the TwoThirds Rule is employed to avoid aliasing of the advection term. Without this option, advection is computed at the specified resolution, which can lead to aliasing on the highfrequency end of the Fourier spectrum if insufficient modes are included in the computation. 21 APRIL 2009:  Repaired an error in the advection term calculations for SE/Fourier 3D simulations. The velocity field (u,v,w) components were being incorrectly backwardstransformed into real space (derivative terms were unaffected). 7 APRIL 2009:  Reduced to 2nd order the diffusion term of the highorder pressure boundary condition (this preserves 3rdorder accuracy in time for the velocity field, Karniadakis & Sherwin, 2005). Attempted implementation of a "twothirds rule" to eliminate aliasing in Fourier space due to quadratic terms in the advection substep (SE/Fourier computations). 6 APRIL 2009:  Modified RAND so that higher modes have a smaller level of random noise applied. This is intended to reduce the effect of instability caused by a cascade of whitenoise energy into the highest Fourier modes. 5 APRIL 2009:  Altered the way symmetry boundaries are enforced in SE/Fourier 3D computations. Now the velocity field is transformed into real space, the symmetry conditions are enforced on each plane, and then the fields are transformed back into Fourier space. It is hoped that this is more stable than the previous implementation, which was causing problems when the highorder pressure BC was employed. 2 APRIL 2009:  Performing the L2 norm calculations with double precision real arithmetic instead of complex arithmetic  this is intended to attempt to overcome the precision issues detected in l2 norm convergence studies from SE/Fourier simulations.  Removed the highorder Neumann pressure boundary condition on symmetry boundaries, which should be exactly zero anyway. This was done to eliminate a spurious fuzziness in solutions detected by Stuart Cogan. 1 APRIL 2009:  Fixed a rare bug in TECP for SE/Fourier simulations. If the velocity components were being plotted in addition to a userspecified field, the ucomponent of velocity was being incorrectly transformed from Fourier to real space. This has been fixed.  Slightly tweaked the "RAND" command for SE/Fourier computations. Complexconjugate copies of positive modes to their negativefrequency counterparts is now done for the whole velocity field, rather than just the randomized parts. This ensures that the conjugate symmetry of the Fourier transforms are preserved. 31 MARCH 2009:  Added a command "PBC" which toggles the highorder pressure boundary condition on or off (default on).  Added a userspecified function plotting capability to the Tecplot routine (this is activated using the "u" option). 30 MARCH 2009:  Chris Butler reported that the L2 norm is still displaying singleprecision convergence in SE/Fourier computations, despite other integral quantities demonstrating doubleprecision convergence.  Fixed a problem reported by Nick Boustead with the new LOAD/SAVE commands: the code was incorrectly determining the number of data fields written to restart files for perturbation fields when no wvelocity was active in the base flow. 27 MARCH 2009:  Added the particle ID number to "TRACK SAVE" output from particle tracking in hexahedral computations.  A compiler optimization error in the Windows version of Viper was overcome by adding a "/Qtrapuv" option to force initialization of saved variables.  In order to improve the precision of the L2 norm integration in SE/Fourier computations, all instances of SQRT(), ABS(), SIGN(), MIN() and MAX() in the code which operate on doubleprecision REAL or doubleprecision COMPLEX data types have been replaced by their specific doubleprecision routine (e.g. DSQRT in place of SQRT, etc.). 20 MARCH 2009:  The SAVE and LOAD routines have been revised. A new format is now in use. Users wishing to SAVE/LOAD using the previous format can do so by calling SAVE or LOAD with the new "old" option specified. In addition, if a user attempts to call LOAD for an old restart file without this option, the code returns an error and attempts to load the data using the old routine anyway. The new routines are more flexible, allowing new facilities such as saving and loading solutions with scalar fields active, safer loading of 2D solutions onto SE/Fourier solutions and vice versa (e.g., loading an SE/Fourier solution onto a 2D simulation loads in the zeroth (or fundamental) mode). In general it is cleverer, as each field is clearly identified in the file, so Viper has a better idea of what it can possibly do with each field. 15 MARCH 2009:  The SE/Fourier axis filter for cylindrical computations has been disabled by default. Users can still activate a filter by setting the "f" option in the FOURIER command. 14 MARCH 2009:  The axis filter in SE/Fourier computations was found to slightly shift the Kovasznay flow solution from its exact value. Suggest users do not use the filter (i.e., explicitly set the "f 0" option in a FOURIER call in AXI computations.  Fixed the SE/Fourier singleprecision convergence issue: problem was caused by generic FORTRAN functions for extracting real & imaginary parts of complex numbers, and for assemlbing a complex number from two real parts. Some of these were not preserving the KIND=8 double precision (64bit) floating point precision. Have replaced all REAL() with DBLE(), CMPLX() with DCMPLX(), AIMAG() with DIMAG() and CONJG() with DCONJG().  While searching for the convergence issue, replaced the EXTERNAL PARDISO calls with a "USE MKL_PARDISO" call to the MKL FORTRAN 90/95 interface for the routine. This picked up a couple of INTENT statements that could have caused problems.  Removed the "skip matrix solve if RHS=0" conditional check in sparse solver routines. This should never occur anyway. 13 MARCH 2009:  Encountered an optimisation or compiler bug under Windows  incorrect (or at least imprecise) results were computed when degree 2 or 3 elements were used.  Refined the code for computing integrals from SE/Fourier results using the INT command.  Added further warning messages to the code used to parse the Viper configuration file  more errors are now detected and reported to help users confirm that their boundary conditions, etc. are being processed correctly. 12 MARCH 2009:  Added a warning message to detect if a "btag" command is assigned to a boundary which is not included in mesh file.  Added a warning message when parsing "viper.cfg" files  the code now complains if an unrecognised variable name is supplied in a "btag" statement.  Streamlined the code calculating maximum changes in velocity. for display each time step. New approach should be faster (a square root is now performed only on the largest "du", "ds", etc., not the whole list of velocities. 10 MARCH 2009:  Altered the implementation of the Boussinesq approximation  it is now based on a principle of calculating the effect of changes from reference temperature & density. 9 MARCH 2009:  Chris Butler found a rare bug in the "simplify_function_string" code, which appeared for functions which had a number of components precisely matching the size of the storage arrays for this information. This has been fixed. 7 MARCH 2009:  A couple of variables in the parallel part of the SE/Fourier time step loop were not designated as "PRIVATE" (or separate copies per thread). This may partially explain the "max du" convergence issue.  Corrected a problem with scalar diffusion  a rouge "Nscalar_steps" variable was not deleted since the transition to a 3rdorder backwards multistep integration scheme for the scalar field. This was causing the scalar field to diffuse incorrectly. 3 MARCH 2009:  Increased the size of the output of a function insertion routine in "usr_vars.f90" to permit the handling of very large compounded mathematical expressions.  Replaced statically allocated storage vectors in "simplify_function" routine in "math_parser.f90" module for more efficient handling of large mathematical expressions supplied by the user. 2 MARCH 2009:  Increased the allowable function string size to approximately 10,000 characters. This permits users to compound many userdefined functions into larger expressions. Storage for these arrays is now dynamic: the hardcoded allowance for 500 boundary is no longer in place.  Fixed a bug in the boundary assignment code: when processing "viper.cfg" files, if multiple "btag" statements duplicated a boundary definition, the code incorrectly defined the boundary  the code now robustly assigns boundaries according to the last of any duplicated boundary assignments. 28 FEBRUARY 2009:  Corrected an issue where the pressure field was being incorrectly plotted in Tecplot dumps from SE/Fourier computations (the negative Fourier modes were being corrupted  this was particularly noticeable if a LOAD operation was performed. 27 FEBRUARY 2009:  Fixed a problem with the SE/Fourier Tecplot output algorithm: the "cartesian" option was not functioning properly when computations were carried out in cylindrical coordinates. 25 FEBRUARY 2009:  Success! Tests confirm that the new version properly indexes the highorder pressure boundary conditions, and also permits time integration to proceed without the erroneous restriction in time steps.  Stu identified a problem in which time integration stability had decreased since the upgrade to the Neumann BCs implementation. This was traced to an indexing problem which was scrambling the boundary nodes on which highorder pressure BCs were applied. This has been corrected, and tests are underway to see if this rectifies the time step restriction problem. 24 FEBRUARY 2009:  Detected an allocation error in the scalartransport routine  this has been fixed.  Improved the "gvar_movref" facility  the change is now calculated as a 3rdorder time derivative of velocity at the appropriate time, and this acceleration term is imposed on the intermediate velocity field during the advection solve. 23 FEBRUARY 2009:  Changed the scalar field advection/diffusion transport algorithm to a 3rdorder backwards multistep method (consistent with velocity field).  Fixed a bug in the 2D Tecplot binary data file generation routine which only arose if the "SR" variable was requested.  Fixed a pointer association error with a 3D pressure boundary condition vector. 21 FEBRUARY 2009:  Fixed an indexing error in the cylindrical SE/Fourier Tecplot routine, which was causing the strain rate and lambda_2 fields to be corrupted (particularly near the axis. 20 FEBRUARY 2009:  Strain rate magnitude and lambda_2 fields are still strangely speckledy, despite the velocity, vorticity and velocity gradient fields being smooth. This is only present in SE/Fourier plots generated from data in cylindrical coordinates... currently searching for the problem.  Identified that the crashing in SE/Fourier computations in cylindrical coordinates was caused by a dividebyzero in a component of the highorder pressure gradient condition imposed on Neumann boundaries  initial tests indicate that this correction has fixed the SE/Fourier cylindricalcoordinates crash recently plaguing the code. 18 FEBRUARY 2009:  Identified that the thetaderivativeterms of the rateofstrain tensor used for strain rate calculations was being incorrectly computed. This is being rectified currently.  Still searching for possible problem with SE/Fourier cylindricalcoordinates shear rate issue  lots of scrambled noise superimposed onto data for some reason.  Tightened file creation in Tecplot routine: existing files are tested to see if they can be overwritten immediately before data written to file  thus there is less chance that this status will change between the file check and the new file creation. 16 FEBRUARY 2009:  Investigating a possible problem with the "SR" field in SE/Fourier computations.  Added a command "gvar_init_scalar_field", which can be used to set an initial condition for a scalar field (similar to "gvar_init_field" for velocity and pressure).  Fixed a bug with STOPCRIT in SE/Fourier computations  it was not stopping the time integration loop.  Fixed some typos in the HELP facility (gvar_init_field had nothing to do with setting the nonNewtonian viscosity function). 15 FEBRUARY 2009:  Neumann BCs now activated for velocity components, pressure, & scalar fields in 2D and 3D computations. This is not yet active in SE/Fourier computations. 13 FEBRUARY 2009:  Began the rollout of Neumann boundary conditions for velocity, pressure and the scalar field. Neumann boundary conditions impose the outward normal gradient of a quantity (e.g. dp/dn) at a boundary, rather than the value itself (as with Dirchlet boundary conditions). These are selected using boundary type #2 (formerly used for timeindependent Dirichlet conditions). Neumann boundaries can be specified as a mathematical function, just as for Dirichlet (type #1) boundaries. Currently this is implemented for velocity only (requiring 2 or 3 components for normal gradients of u,v,w fields). Pressure and scalar field Neumann boundary capabilities are coming. This feature will be useful for imposing flux conditions in scalar field computations  particularly Boussinesq approximations of densitygradientdriven flows. 12 FEBRUARY 2009:  Identified and corrected a couple of errors relating to the calculation of velocity gradients and shear rate fields in the SE/Fourier version of TECP with the "vars" option active. 9 FEBRUARY 2009:  TECP "vars" option is now operational for 2D, 3D, and SE/Fourier simulations. Velocity gradient variable names are now correct for both cylindrical and Cartesian coordinates. 7 FEBRUARY 2009:  Velocity gradient variables added to 2D & 3D Tecplot files output from TECP using "vars" option.  Removed the "o" option in 2D & 3D Tecplot output with TECP. This functionality has been replaced with the "vars" option. Still need to add velocity gradients in 2d/3d TECP routines. 6 FEBRUARY 2009:  Rolled out an option "vars" in the TECP command (currently SE/Fourier only), which allows users to select which of a number of different variables they wish to include in a Tecplot data file. The "sr" option has now been removed. This new option will eventually replace the seldomused "o" option. 5 FEBRUARY 2009:  Fixed a bug in the boundary curvature algorithm which was failing to correctly curve boundaries which comprised two 2D element edges. 15 JANUARY 2009:  A bug was detected with the Floquet solver when base flows were frozen, that had emerged during a recent alteration to the way that base flow velocity fields were distributed between threads. This has now been corrected. A vector copy was being skipped accidentally when "FREEZE" was active. 9 JANUARY 2009:  Added option "sr" to TECP command, which can be used to output the shear rate field in an SE/Fourier computation. 8 JANUARY 2009:  Added capability of outputting only a single Fourier mode in SE/Fourier computations with the new "m" option in the TECP command. 7 JANUARY 2009:  Added "cylindrical" and "cartesian" options to the TECP and TEC_FLOQ commands. For SE/Fourier 3D computations, and 3D reconstructions of Floquet modes, these options can be used to determine whether the velocity components in the Tecplot data files are the cylindrical or Cartesian components. The Cartesian form can be useful for plotting velocity vector fields in Tecplot (which natively uses a Cartesian coordinate system for plotting).  Removed the particle concentration field from Tecplot plotting of SE/Fourier solutions as it was interminably slow to compute. 2 JANUARY 2009:  Parallelised the particle tracking time integration routine. Testing indicates this has been successful, and will produce a solid speedup for particle tracking simulations.  Observed that the TECP output of SE/Fourier computations when particle tracking is active is interminably slow. Attempting some speedups and parallelisation to help, but may have to rely on TRACK SAVE for plotting.  Fixed a couple of typos in the HELP documentation.  Noticed that some OpenMP statements in the source code were incorrectly decorated as !OMP rather than !$OMP, and were therefore not activating. These were only intended to activate when singlefield computations were being performed, so this does not effect the Floquet analysis and SE/Fourier parallelizations. 26 DECEMBER 2008:  Added time "t" to the variables that can be adjusted using the "set" command.  Added the capability to include an "=" sign in "set" expressions, and have also now added the possibility of changing "RKV", "dt" and "t" variables directly on the Viper command line, e.g. "t = 50", "dt = 0.005", "rkv 100", etc. 23 DECEMBER 2008:  Fixed a bug with the "gvar_lorenz" command, which was not correctly evaluating the function during time stepping. 15 DECEMBER 2008:  Added underrelaxation and additional tolerancing to the routine used to determine the parametric coordinates within an element of a physical coordinate on the mesh. This is designed to resolve problem of some points very near to a boundary being erroneously identified as lying outside the domain. 14 DECEMBER 2008:  Tests confirm that the parallelisation bug in the Floquet solver has been fixed. 13 DECEMBER 2008:  Altered the way base flow velocity field data is passed across threads during parallel stability analysis  testing underway to determine if this fixes the aforementioned bug.  Identified a problem with the Floquet solver when running in parallel. If multiple fields are being computed per thread (e.g. 8 fields over 4 threads), then the multipliers returned for the perturbation fields computed on the same thread as the base flow are nonsensical. This is being looked into currently. 11 DECEMBER 2008:  Added the particle ID number to the output of "TRACK SAMPLE". 10 DECEMBER 2008:  Recoded the "AUTOCORRF" routine  the returned autocorrelation is now normalised (that is, mean is subtracted from the input signals, and the resulting correlation is divided through by the variance). This means now that the returned correlation will always vary between 1 (correlated), through 0 (uncorrelated) to 1 (inversely correlated). 8 DECEMBER 2008:  Added two new commands to be used to facilitate magnetohydrodynamical modeling: GVAR_LORENZ can be used in the "viper.cfg" file to express functions for the components of the Lorenz force, which is then calculated and added to the computation of a 2D fluid flow. QUASI2D can be used within Viper to establish a "quasi2D" treatment of a 3D flow by modeling it using the 2D solver with the addition of a friction term, subtracted to mimic the effect of friction on the walls of the domain in the outofplane direction. 5 DECEMBER 2008:  The command "sample" has been improved  it should now work for SE/Fourier computations.  Tightened scratch file creation/removal code in "loop" command  a file that was no longer written to since yesterday's update is no longer created. 4 DECEMBER 2008:  Added a new function to the mathematics parser: "rand(x)". The function returns a random number between 0 and x, and is always treated as a time and spacevarying function. That is, a different random number is calculated at each node where the function is evaluated, and at each time that the function is evaluated.  Further pointer association problems with particle tracking have been fixed. Now Viper is more robust to "track" calls appearing either before or after "init".  Modified the "loop" code to create smaller scratch files storing looped commands. These are invisible on Windows systems, but are visible on Linux systems. Nevertheless, if a very large loop is constructed, a significant pause could result as the scratch file containing the unrolled loop commands was created. Now these files are much more compact, as the loop counting is handled by Viper, and the commands are not repeated in the scratch files.  Added screen output during loops informing the user how many loop iterations remain. 3 DECEMBER 2008:  Addressed a bug with "track seed" for SE/Fourier computations  the zdirection pointers were not being associated properly.  Added particle concentration field to Tecplot output of SE/Fourier 3D computations. 2 DECEMBER 2008:  Slightly modified "max du" output during time stepping: an extra blank has been added to clear any extra characters from the line when the next time step is performed. 28 NOVEMBER 2008:  In ARNOLDI the limitations on number of eigenvalues being sought and the number of Arnoldi vectors in a computation (formerly 12 & 30, respectively) have been removed. Storage is dynamic, so these limitations are redundant.  Slightly tweaked the format of output of floatingpoint numbers to get rid of annoying blank spaces in output. 25 NOVEMBER 2008:  Have modified the Tecplot plotting routines and the particle tracking routines to rectify some issues with SEFourer particle tracking not following the flow properly. 21 NOVEMBER 2008:  Observed that particles were not following the flow precisely when flowing across an (rtheta) plane in cylindrical coordinates. This is being corrected. 20 NOVEMBER 2008:  Fixed some bugs relating to the plotting of SE/Fourier computations, as well as particle tracking in SE/Fourier computations  particularly in a cylindrical framework. 19 NOVEMBER 2008:  Implementation of the particle tracking algorithm in the SE/Fourier 3D flow solver has been completed. The particle concentration field in Tecplot output has not yet been implemented for these computations. The track_pts file should contain points in the coordinate system being computed in (i.e. xyz for Cartesian, zrtheta for cylindrical). 18 NOVEMBER 2008:  Beginning to roll out an extension of the particle tracking algorithm to the SE/Fourier code. 17 NOVEMBER 2008:  Implemented the Neumann highorder pressure boundary condition in computations of the perturbation fields in the stability analysis solver, and in spectralelement/Fourier 3D computations. These solutions should now be formally 3rdorder accurate in time. 13 NOVEMBER 2008:  The issue with ARNOLDI producing quasiperiodic modes may be a roundoff error issue. Test cases suggest the imaginary component is very small. Further investigation underway.  For ARNOLDI, when base flows have 3 components (using WVEL), the complex matrix capabilities of the ARPACK package are now being used. It has been shown that this produces the same results as the previous treatment. This revision to the code has modified the Arnoldi restart file created by Viper (it is now substantially smaller)  users will not be able to restart from Arnoldi runs from earlier versions of the code. 12 NOVEMBER 2008:  Added extra output to ARNOLDI routine: the error/information messages reported by the ARPACK subroutines are now output to screen. This information is provided to the user as the ARNOLDI iterations can occasionally fail for some combinations of parameters, etc.  Stuart Cogan reported that ARNOLDI is returning complex Floquet multipliers when the power method predicts real multipliers during cylindrical computations with swirl (nonzero azimuthal velocities). This is being investigated further. 13 OCTOBER 2008:  Added a new functionality to RAND: now using the k option, randomisation can be applied to a single mode. 10 OCTOBER 2008:  Fixed a small bug where some outofrange integers were incorrectly displaying as negative numbers during startup and initialisation for very large jobs. This did not effect the flow calculations. 7 OCTOBER 2008:  A bug was detected in the SE/Fourier algorithm: When timedependent boundary conditions were used during a parallel simulation, the Discrete Fourier Transform package used to calculate the Fouriertransformed boundary conditions returned incorrect results. The Fourier transforms are now performed outside the parallel loop. 30 SEPTEMBER 2008:  Fixed a bug in the Tecplot Floquet reconstruction routine  in cylindrical coordinates, the radial and theta (v & w) components of velocity are now output in cylindrical coordinates. 26 SEPTEMBER 2008:  A bug in the Tecplot plotting routine has been addressed, where vorticity components in cylindrical coordinates were being incorrectly computed.  The TEC_FLOQ routine has now been updated to include velocity components.  Reintroduced a filter to the SE/Fourier modes  the highestfrequency modes are forced to be zero  the complete removal of the 2/3rds rule yesterday resulted in unstable computations.  Added a command "AUTOCORRF", which outputs the spanwise autocorrelation of the velocity components at a sampled point on the spectralelement mesh.  Found and rectified a bug in the "SAMPLEF" routine  an incorrect reference to v & w velocities was corrupting the results. 25 SEPTEMBER 2008:  Removed the "2/3rd rule" filter applied to the outofplane Fourier modes in SE/Fourier computations. This was introduced during implementation of the scheme in an attempt to stabilize computations in cylindrical coordinates, though a separate radial filter is also applied in those cases, so this filter was unnecessarily limiting. The 2/3rd rule requires that the highestfrequency 1/3rd of the Fourier spectrum be rendered equal to zero to guarantee that aliasing is not occurring (aliasing is the erroneous appeaerance of energy in highfrequency modes due to insufficient resolution in a Fourier transform. *** Users should contact Dr Greg Sheard if this causes problems in SE/Fourier calcs ***  Added a new command "ENERGYF", which outputs to a text file the integral norm of the energy in each Fourier mode of a spectralelement/Fourier computation. 23 SEPTEMBER 2008:  Added a command SAMPLEF, which can be used to output the Fourier coefficients of the velocity field at a point in the computational domain during SE/Fourier computations.  Altered the behaviour of the RAND command in SE/Fourier computations  now the imaginary components of the nonzero modes are also randomised. 16 SEPTEMBER 2008:  An immersedboundary feature has been added to the code  this experimental feature currently synchronises with an external algorithm that tracks a boundary immersed in the flow. 9 SEPTEMBER 2008:  A memory deallocation bug was preventing repeated calls to "init" since the OpenMP parallelization of recent months. This has been fixed. 8 SEPTEMBER 2008:  A bug was reported with the Arnoldi routine  on Linux systems the code crashes while writing Tecplot files. The bug was isolated to an OPTIONAL argument of the Tecplot output subroutine, which was not being treated properly. The Arnoldi routine did not supply this argument, causing its value to be undefined. This has now been fixed.  A bug was reported in the cylindricalcoordinates stability analysis solver, where an incorrect function argument was causing the code to fail without explanation. This has been fixed. 14 AUGUST 2008:  Fixed a bug in the SE/Fourier implementation of the "forces" command  previously zero forces were output  now forces are computed from the fundamental mode of the Fourier expansion  this is not currently correct for the cylindrical formulation. 13 AUGUST 2008:  Added a Boussinesq approximation for buoyancydriven convection to the 2D and 3D hexahedral solvers. This feature can be activated using the BOUSS command, and requires that a scalar field is being computed, which acts as the temperature field. 6 AUGUST 2008:  Added a counter to the output of the step command. This helps the user identify how much longer the currently requested steps have to complete.  Fixed an error relating to flow at the axis which was affecting the axisymmetric solver. This error had emerged in the restructuring of the code during the SE/Fourier implementation. The code now strongly enforces zero Dirichlet boundary conditions on the axis for the v & wvelocity components. 4 AUGUST 2008:  Restructured calculation of advection substep throughout the code. Now the velocity fields are extrapolated to time t+dt, then the RHS of the advection term is computed. Previously, extrapolation was conducted from stored RHS vectors from previous timesteps. This approach reduces memory overhead slightly, and also simplifies the code when simulations are initialized and restarted. 1 AUGUST 2008:  Added a command, MASK, which multiplies a velocity field by a specified function. This command can be used to filter or scale velocity fields. 30 JULY 2008:  Two new commands have been added. MESHPTS outputs the global mesh coordinates to a text file, and VISMAT (under development) will generate image files showing the structure of the matrices being solved by the code. 16 JULY 2008:  Added OpenMP constructs to advection, pressure & diffusion time integration routines, with conditional "IF" statements to be called only if a single field is being computed. This should improve scalability of simple two or threedimensional base flow computations. 12 JULY 2008:  Tests have been showing that ROTATE was not functioning correctly. A test case was established whereby a vortex flow with and without a bulk rotation was analysed for threedimensional stability both with and without the ROTATE command being called. This enabled the functionality of the command to be corrected. Tests on unequal strength vortex pairs will continue. 25 JUNE 2008:  Fixed the symmetry boundary condition assignment  these were not being detected following the alteration on 14 May 2008 to the way in which Viper processed Dirichlet boundary conditions.  Fixed a minor bug in the ROTATE implementation  when base flows have a nonzero wvelocity, the code now correctly includes the imaginary u & v components of the perturbation field when evaluation the Coriolis correction. 18 JUNE 2008:  Upgraded ARNOLDI stability analysis solver to compute the stability of perturbation fields both with and without a wcomponent of velocity in the base flow (previously only w=0 flows were implemented). 13 JUNE 2008:  Found a bug in the ROTATE routine  the xdirection advection RHS vectors were being copied into both the x and ydirection vectors. Tests of the fix to this suggest that the code is working better now. 12 JUNE 2008:  Revising the rotating reference frame code for the perturbation field. Removed centrifugal acceleration component as this appears only in the integration of the base flow.  Tidied up some of the outputting of floatingpoint numbers in scientific notation  tidier notation used for more values reported during initialisation. 6 JUNE 2008:  A small performance boost was achieved in parallel by using separate copies of the spatial derivative matrices for each processing unit. 3 JUNE 2008:  Investigating the use of KMP_AFFINITY and extra OMP loops during initialisation to get improved parallel performance on a perprocessor basis. Thus far have sped up PARDISO computations, but other parts have slowed  may need to create perthread copies of derivative matrices, etc. 30 MAY 2008:  Early parallelization tests for the stability analysis code indicate a promising speedup of 4.7 times over 8 CPUs, and 6.1 times over 16 CPUs.  Moved time evolution of perturbation fields into a subroutine  this will aid parallelization of the 2D time integration code. 29 MAY 2008:  Condensed some redundant code in pressure and diffusion solves  now using one routine for all 2D & 3D static condensation and matrix solve phases of the pressure and diffusion substeps, rather than the 7 separate routines that were being called earlier. 28 MAY 2008:  Identified that the cylindrical SE/Fourier 3D solver was suffering from an incorrect calculation of thetaderivatives during the advection step. This was contaminating the results and leading to a spurious deviation of the flow near the axis, as well as instability. This has now been fixed. Tests against the Kovasznay flow solution verify that the solver is now functioning correctly. 22 MAY 2008:  Tested the Cartesian spectralelement/Fourier 3D algorithm against an analytical test case  a Kovasznay flow  imposed oblique to the domain. The test verified that the Cartesian formulation is functioning correctly. Tests indicate that the cylindrical formulation is not yet correct, though is stable  error manifests as a slight discrepancy across the axis.  Identified a stack access violation under Windows that was causing Viper to crash during calls to "ARNOLDI". A function "second" was being called while no longer being defined  this has now been removed, as we are not utilising any timing statistics from the ARPACK package.  Migrated compilers to Intel Fortran 10.1, and Intel MKL 10.0. This caused minor hiccups due to minor alterations in compiler options, and a problem with the unsymmetric matrix solver implemented in the MKL (which affected simulations with no Dirichlet pressure boundaries). These problems have been corrected (using structurally symmetric matrices instead), and the code is now functioning normally. 20 MAY 2008:  For SE/Fourier computations in cylindrical coordinates, an instability can develop near the axis due to outofplane spatial resolution going to infinity as r > 0. A filter has been constructed that filters all modes higher than the first mode towards zero approaching the axis. The filter begins acting within the nearest 10% of the domain to the axis. 19 MAY 2008:  Fixed a couple of small bugs in Tecplot output routine (involving sequenced numbering and uninitialised variables), as well as the time stepping routine for SE/Fourier 3D computations. In particular, the Dirichlet boundaries were not being carried forward in the transformed sense for cylindrical computations. This has been fixed. 18 MAY 2008:  Fixed some bugs in the Tecplot plotting routine for SE/Fourier computations. Flow fields now closely resemble expected flow fields for test cases. 16 MAY 2008:  Further work achieved a speedup of approx 7.5 over 16 processors. Still attempting further optimisations.  Parallelization of pressure & diffusion substeps resulted in a speedup over 16 cpus of 3.2 times. When part of the advection term was parallelized, a speedup of 6.7 times was achieved. Advection is the bottleneck (pressure and diffusion each achieve a speedup of approximately 14 on 16 cpus, whereas advection currently achieves about 3.3). Work is continuing to improve these figures further. 15 MAY 2008:  Added OpenMP parallelisation of the time stepping loop for the 3D spectralelement/Fourier algorithm. Running tests to determine the effectiveness of this parallelisation. 14 MAY 2008:  Updated the way in which Viper reads boundary conditions. All conditions are input as mathematical functions, and Viper determines whether they are timedependent, spatially varying, or constant, and computes them accordingly. 12 MAY 2008:  SE/Fourier implementation coming together steadily. Save/load, Tecplot, L2, flowrate, monitor capabilities implemented. Still need to implement full boundary condition assignment capabilities  currently must read in as part of a 2D restart file. Testing of cylindrical solver still required. Forces still required.  A rewrite of boundary conditions is being considered, whereby all Dirichlet conditions would be read in as mathematical functions, and Viper will ascertain which are timedependent (to be evaluated during time integration), and which are timeindependent (to be evaluated during initialisation). This will be incorporated during the rollout of the SE/Fourier algorithm. 8 MAY 2008:  Rolled out a provisional version of a spectralelement/Fourier 3D flow solver (in both Cartesian and cylindrical coordinates). Still need to complete boundary condition assignment, and postprocessing capabilities. 3 MAY 2008:  Added command ROTATE, which is designed to correct the evolution equations for frozen perturbation fields during 2D Cartesian stability analysis for the rotating reference frame in which they would effectively be computed in. 29 APRIL 2008:  Modified the Tecplot output routines so that the binary files are generated by Viper, rather than using the supplied "tecio" library. Viper now generates Tecplot binary files readable by Tecplot versions 10.2 or later. Users with earlier versions should use the ASCII output option (see HELP TECP). 28 APRIL 2008:  Tecplot 360 (2008) has altered the functions provided in the tecio.dll routine from the previous 2006 version. If users run Viper (which was compiled using the 2006 "tecio" library) while having Tecplot 360 2008 installed will be confronted with an error when calling "tecp". I am now contemplating writing my own routines to save Tecplot binary data, which could be made readable from a number of Tecplot versions. 5 MARCH 2008:  Fixed a Tecplot plotting bug  the velocity divergence (grad_u) was being incorrectly calculated in cylindrical coordinates. This has been fixed, and this problem did not affect the solver, which handles divergence correctly. 28 FEBRUARY 2008:  Added an option "t" to the Tecplot output routines, which enables ASCII output in Tecplot format rather than binary. These files can be read by older versions of Tecplot, and may be used by other visualization programs more easily. 15 FEBRUARY 2008:  Fixed a bug in MONITOR, where 2D flows with a wvelocity component active were not written with the wvelocity component included. 5 JANUARY 2008:  Used the modular storage of global variables in the ARPACK routines to save the state of an Arnoldi iteration at each call to ARNOLDI. This allows for resumption of a simulation at a later point. 4 JANUARY 2008:  Cleaned up the ARPACK module, and replaced variables stored using the FORTRAN "SAVE" command with variables stored in separate modules. 14 DECEMBER 2007:  Added a command SAMPLE, which takes the spatial coordinates of a point in the computational domain, and outputs to file the interpolated values of velocity, velocity gradients, strain rate magnitude and pressure. 29 NOVEMBER 2007:  Added convergence output to the ARNOLDI command, so that users are given some idea as to the progress of the computation. 28 NOVEMBER 2007:  Added ability to specify a filename prefix for use with the ARNOLDI command to allow a unique set of files to be stored, rather than simply the default.  Fixed a bug with the ia32 versions of the ARNOLDI command, where an unused external timing command was being called as a subroutine rather than a function. Removed all calls to this function. 19 NOVEMBER 2007:  Implemented an Implicitly Started Arnoldi Method to find the complex eigenvalues (Floquet multipliers), and eigenvectors (Floquet mode velocity fields) corresponding to the matrix operator representing time integration of the linearized NavierStokes equations. This is implemented through the "arnoldi" command, which can be used in place of the "stab" command (after a call to "floq") to perform linear Floquet stability analysis. 17 OCTOBER 2007:  Fixed an issue with the Tecplot calculation of perturbation field vorticity. When a fully complex expansion was used, some of the zderivatives were not being correctly computed, which caused havoc for the calculation of perturbation field strain & vorticity. 16 OCTOBER 2007:  Added further simplifications to the function simplifier  now removes redundant brackets around variables as well as numbers. 15 OCTOBER 2007:  A bug in the function parsing code was found, whereby components of variable names were being substituted in a function expression by a matching variable name  instead, only matching FULL NAMES should be substituted!!! This has been fixed, and the displaying of the functions to screen has been streamlined. 11 OCTOBER 2007:  Found and fixed a frustrating bug in "LOAD" which was causing the wvelocity component of the currenttime perturbation field to be incorrectly read. The physical quantities were being replaced by garbage. This was also rendering attempts to load perturbation fields prior to calling INIT futile, as only zeroes were being input, which were promptly normalized to infinity when the code attempted to set itself up for Floquet analysis time integration. 10 OCTOBER 2007:  Fixed a sequential file numbering problem. Calls to "TECP" and "TEC_FLOQ" were accidentally both incrementing the same counter within the code. 9 OCTOBER 2007:  Improved plotting of the "max ds" quantity, the maximum change in the scalar field from one time step to the next. It was being incorrectly calculated previously, and was therefore always O(1) in size, even when the flow and scalar field converged to a steady state.  Altered output format of time "t" and "max d?" quantities. These now use the "G" edit descriptor in FORTRAN, which produces more readable output (i.e. only uses scientific notation if numbers are very large or very small). 8 OCTOBER 2007:  Found and fixed a small issue with the math parser function simplification routine. "If" commands (due to the comma) were being incorrectly processed. 7 OCTOBER 2007:  Shifted searching through elements for Neumann pressure BCs from within time stepping code to the initialization code. Thus should result in a small speedup in time integration. 5 OCTOBER 2007:  Scope for a further 10% speedup has been identified for the evaluation of highorder Neumann boundaries for pressure. These will be implemented shortly.  Successfully implemented a speedup in the evaluation of timevarying user defined boundary conditions. If the BCs are not spatially varying, then they are only evaluated once, rather than for every node. This has resulted in measured speed increases of 82% in some vortexinteraction simulations. 30 SEPTEMBER 2007:  Modified the source code varibale naming of wvelocity in the perturbation field, to acknowledge that the wvelocity field is imaginary when a zvelocity is not active in the base flow. This has made the code read more clearly, and now the reduced and fully complex expansions of the Floquet modes have been coded up consistently. Now both are producing the same Floquet multipliers for some simple test cases, in both cylindrical and Cartesian coordinates. 29 SEPTEMBER 2007:  Have attempted a swap of the sign of the changeofvariables in the diffusion step for a Floquet mode in cylindrical coordinates with z velocity active  will see if this produces results consistent with simulations without an active zvelocity in the base flow.  Fixed a small bug in the 3D Tecplot Floquet mode reconstruction routine. The scaling factor is now consistently applied to the perturbation field and the corresponding derivatives correctly.  Performed some tidying up of the code: The separate eigenvalue/vector routine used to calculate the strain fields for ia64 Linux platforms has been replaced by the standard code, as the floatingpoint exception errors that were occurring have been avoided by explicitly setting the "fpe3" flag at compile time. 28 SEPTEMBER 2007:  Corrected the vorticity components for the "TEC_FLOQ" routine when using cylindrical coordinates. The vorticity components are now calculated as rotation about each of the cylindrical coordinate axes, not (x,y,z) axes.  Developed a new routine for outputting the perturbation fields of Floquet modes. The new command "TEC_FLOQ" can be called to generate a threedimensional Tecplot file containing a reconstruction of the vorticity field acquired when the 3D Floquet mode is superimposed on the 2D base flow. This command works in both Cartesian and cylindrical coordinates, as well as for base flows with or without an active zvelocity component. 27 SEPTEMBER 2007:  Stabilized finitezvelocity Flqouet analysis in cylindrical coordinates: problem lay in the changeofvariables applied in the diffusion term. Code still giving incorrect multipliers in cylindrical coordinates: testing indicates source of error is not likely the advection step. Problem currently under investigation.  Modified the SAVE and LOAD commands to output and read in the imaginary components of the complex perturbation fields when the z velocity is active in the base flow.  Tests showed that When a nonzero velocity was present in a 3component base flow, the perturbation fields were unstable in cylindrical coordinates. Further testing underway. 26 SEPTEMBER 2007:  Tests of the Cartesian formulation of the complex spanwise expansion in the Floquet solver (with nonzero spanwise base flow velocity) indicate that Floquet multipliers may be being correctly calculated. Further testing underway. 25 SEPTEMBER 2007:  For some reason, the HELP entry for the SCALAR set of commands was missing. This has been updated, and the Viper Reference Manual has also been corrected to reflect this change. 24 SEPTEMBER 2007:  Modified the command interface, so that if macro or loop commands are being executed, they are displayed on the command line as they are called.  Implemented complex Fourier mode expansion of Floquet modes if a nonzero wvelocity is present in the base flow. Testing is underway. 18 SEPTEMBER 2007:  Added a command STOPCRIT, which can be used to specify a stopping criterion on time integration based on a critical value of "max_du". Once "max_du" reaches the specified criterion, time stepping is abruptly cessated, and the control passes to the next input command. 16 SEPTEMBER 2007:  Missing terms in the perturbation field advection step for Floquet analysis of flows with swirl or wvelocity were identified; relating to products of the wvelocity and zderivatives of the perturbation. These have been added, and tests are underway to verify the solutions. 12 SEPTEMBER 2007:  Found and rectified a memory allocationrelated bug that emerged during initialisation for Floquet stability anaysis. This bug was caused when uninitialised CSR matrices were being DEALLOCATED. For some reason, they were being initialised with arbitrary sizes, etc., and this was causing runtime errors and segmentation faults across all platforms. 29 AUGUST 2007:  The internal use of the "Re" variable in the FORTRAN source files of Viper has been rolled over to the name "RKV", consistent with the recent alteration to the name of the corresponding parameter. 27 AUGUST 2007:  Stuart Cogan identified a bug in the Tecplot plotting of strain for axisymmetric flows with swirl (only a 2by2 strain matrix was being allocated, whereas the code requires a 3by3 matrix).  The correction to velocity vectors along a symmetry boundary has been modified to avoid correcting velocities along an axis of symmetry in cylindrical coordinates: this condition is imposed naturally as a result of the Galerkin formulation of the problem in cylindrical coordinates, so no further modification is required. 11 AUGUST 2007:  Isolated and rectified the ia64 crashing when evaluating the strain field. The fix is messy  basically the crash was happening whenever the input matrix had zeros in it, so the code performs a crude check for this condition, and returns a zero strain in these instances, though this is sometimes not appropriate. 10 AUGUST 2007:  Added an extra timer on the evaluation of Dirichlet boundary conditions for the diffusion substep  this contributed about 45% to the overall compute time for vortex interraction flows, and is therefore a good target for optimization/parallelization.  Changeover from "Re" to "RKV" when referring to the reciprocal kinematic viscosity. This includes "help" files, and userdefined functions. 9 AUGUST 2007:  A number of bizarre errors have been encountered when using very large meshes on ia32 linux platforms. These include integer divide byzero, and others. Some of these may be related to the external libraries...  Neatened the alignment of output from various routines to improve appearance at the command line. 7 AUGUST 2007:  Migrated ALLOCATABLE TARGET matrices to POINTER matrices in the INIT routine when building Laplacian matrices & their inverses. This reduces the number of ALLOCATE/DEALLOCATE calls, and should then make for faster and more efficient reinitialisation. 4 AUGUST 2007:  Improved GETMINMAX routine  now can find multiple minima or maxima in each element.  Rectified a bug in the LOAD routine  a variable "floq_mode" was being used before being defined. This was causing occasional crashes. 27 JULY 2007:  Attempted to locate a memory leak in INIT, with no success. Leak is only a problem if many INIT calls are made in a single Viper session, which is unusual. 23 JULY 2007:  Added a "build date" to the title screen that appears when the code is invoked, facilitated by the use of the "fpp" preprocessor "__DATE__" macro. 20 JULY 2007:  Parallelized elemental Laplacian construction loop.  Have now parallelized all pressure, diffusion & advection elemental loops. 19 JULY 2007:  Parallelized an elemental loop at the end of the diffusion substep. 11 JULY 2007:  Added some additional OpenMP declarations to loops in the pressure substep, to complement those in the advection step. Presently achieving good speedup from 1 to 2 threads, but no further benefit beyond 2 threads.  Added separate timers for each of the advection, pressure, and diffusion substeps. 6 JUNE 2007 (DDAY):  Fixed a bug in the "forces" command  when pressure gradients (using "pgrad" were imposed on a flow, the pressure component of the force was being incorrectly calculated. 5 JUNE 2007:  Changed the eigenvector/eigenvalue calculation routines to use LAPACK routine "dsyev" instead of "dsyevr", as the previous routine was problematic on the Itanium II architecture on APAC, and the performance benefit in evaluating only selected eigenvectors/eigenvalues was considered negligible here, as our matrices are only order 2 or 3 anyway. 2 JUNE 2007:  Added extra feature to the ADVECT command. Users can now use commands "ADVECT ON" and "ADVECT OFF" to switch on/off the calculation of the advective terms of the base flow. This could be used for timevarying creeping flow computations, with timedependent boundaries, for example. 29 MAY 2007:  On Itanium2 ia64 processors, crashing was observed when evaluating user defined functions as part of the "getminmax" and "int" routines, which incorrectly implemented this facility. This has been rectified, and the erroneous & unpredictable crashing (with floatingpoint errors) has been remedied. 28 MAY 2007:  Ironed out wrinkles in "getminmax" command  the routine had some bugs which either resulted in an incorrect turning point being found as a result of polynomial stiffness, or turning points to be neglected completely. 25 MAY 2007:  Matt Fitzgerald detected an error in TECP, which relates to the computation of "o 3" level fields (strain or lambda_2). Problem stems from a "dividebyzero" in strain directional component evaluation. 23 MAY 2007:  Added a routine that finds and outputs both the physical location, and the value, of a userspecified scalar function. This is invoked by the command "GETMINMAX", and has as an intended application the accurate identification of vortices in a flow (i.e., by calling /> GETMINMAX 'dvdxdudy') 27 APRIL 2007:  The plotting of strain vectors has been improved to more accurately compute vectors at element boundaries. 24 APRIL 2007:  "o" option added to Tecplot output routine. This option allows different levels of output to be selected, from 1 to 3, where 1 is the smallest number of variables (and hence the smallest file size) and 3 is the largest.  Rolled eigenvalue and eigenvector routines being computed as part of the Tecplot routine over to LAPACK. 23 APRIL 2007:  Tecplot output routine modified to fix strain field output. Routine now outputs vector components that give the direction of the strain field (eigenvector corresponding to the largest eigenvalue of the strain tensor), and whose magnitude equate to the largest eigenvalue  the magnitude of the principal strain throughout the flow. 24 MARCH 2007:  Added extra floatingpoint overflow and divide by zero checking in "gll.f90" and "tec_out.f90" routines to eliminate some runtime errors in linux. Code now more robust. 23 MARCH 2007:  Added a config. file command "gvar_movref", which allows users to specify functions for velocity components corresponding to a moving frame of reference. The ability for this routine to handle timevarying functions makes it far more powerful and userfriendly than the "CHREF" command. 8 MARCH 2007:  Fixed a problem with "math_parser" module  some code had not been updated from the latest fix  some incorrect evaluation behaviour was being generated.  An error has been cropping up on APAC  isolated its cause as being a floating point error in the "find_circle_from_three_points" routine. Error due to argument of an inverse cosine being out of bounds. For some reason the Itanium compiler did not pick this up. 5 MARCH 2007:  Dr Stuart Midgley issued a further fix which removed the "Operator following operator" error message in "if(" functions. 2 MARCH 2007:  Made further cosmetic changes to clean up startup and initialization info.  Implemented a fix from Dr Stuart Midgley for the function parser. This has eliminated the improper "Operator following operator" error with "if" functions. 28 FEBRUARY 2007:  Made some (mostly cosmetic) changes to the code in "ti_advect.f90", which in some cases might cause a miniscule speedup in the computations. 27 FEBRUARY 2007:  Dr Stuart Midgley (author of the Mathematics Parser) sent a fix for the "if(" function error messaging (the correct function was still being evaluated), but another error ("Operator following operator") has been produced with expressions of the form "if(x > 1)...". Currently awaiting a fix for this. 17 FEBRUARY 2007:  Fixed a problem with the "loop" command, where long lines of text containing functions were sometimes incorrectly parsed because the inverted commas were being removed from the text in the scratch file. 16 FEBRUARY 2007:  A problem with the "math_parser" library has been found  the package is not accepting nested "if()" functions  raising correspondence with the developer in an attempt to find a solution  otherwise will need to reverseengineer their source code...  Removed change of reference shift of perturbation field velocity in CHREF command: This was causing irregularities in Floquet analysis. It is incorrect to change perturbation velocity field as the change in reference frame is described by the change made to the base flow velocities. 24 JANUARY 2007:  Confirmed with computation of sphere wake at Re=212 that Floquet problem now resolved. Floquet multiplier 1.000 achieved for m=1 mode.  Problem with axisymmetric Floquet code persisted after base flow axi fix. The cause seems to be the incorrect application of radial and azimuthal Helmholtz equations to the transformed coordinates. A fix of this is producing perturbation fields consistent with Natarajan and Acrivos (1993) results. 23 JANUARY 2007:  Fixed problem with 2D/axi skewsymmetric formulation of advection terms. This had crept back in to the solver from an earlier fix. Additional axisymmetric terms were missing a 1/2 factor. Checked with wake behind a sphere  drag forces now correctly computed. 22 JANUARY 2007:  For Tecplot plotting, the code now uses L'Hopital's rule to approximate azimuthal derivatives of perturbation field velocity components on the axis.  Found likely cause of Axi Floquet problem  an attempt to zero transformed vvelocity values on the axis was using the incorrect global numbering.  Fixed a bug with the MONITOR routine  users can now perform multiple INIT calls in a single session without MONITORassigned output files causing the programme to crash. Users can also close existing files during a session, and create new ones.  Identified a problem with the Tecplot routine: Radial component of zderivatives was not included for cylindrical coordinates. This affected most spatial derivativebased output, including vorticity.  Floquet test 2: NO phantom pert field vort present in Cartesian (no swirl) computations with multiple mode numbers.  Floquet test 1: Phantom pert field vort present in AXI (no swirl) computations with multiple mode numbers.  Found some Nglobal constants which should have been Nglobal_u: this could have an effect on flows with periodic boundaries... 20 JANUARY 2007:  Increased amount of information displayed regarding matrix factorisation during initialisation phase.  Detected a problem with perturbation field in axisymmetric computations  appears to be associated with Laplacian or Helmholtzian solve.  Fixed a bug whereby "radial_dist" array was not being constructed for FROZEN Floquet analysis  caused perturbation fields to diverge. 10 JANUARY 2007:  Begun adding !$OMP declarations to parallelise some regions of the code using OpenMP. 5 JANUARY 2007:  Used IFDEF directives to differentiate Viper for Windows & Viper for Linux in "main.f90". 9 DECEMBER 2006:  Used "(*,a)" formatting for string output rather than "(*,*)", which was looking terrible under the Intel compiler, with all lines breaking after 80odd characters. Now initialisation and HELP facility are again legible! Yay!  Detected a problem whereby if illegal variables were parsed in function strings, the code would obliviously continue with incorrect function evaluations. A firm warning message has been added to inform the user when these problems occur. This will drastically improve the robustness of the "usr_var" feature of the code.  Upgraded "math_parser" module from a 2004 version to a 2006 version of the code. 6 DECEMBER 2006:  Identified and rectified a potential bug in TECP routine in which zderivatives might have been miscalculated if WVEL and FLOQ were both active.  Fixed bug in SAVE routine where wvelocity component was not being saved correctly due to a use of the nearobsolete "solverID" tag. 3 DECEMBER 2006:  Fixed an error in Floquet analysis routine where pressure substep was incorrect due to incorrect enforcement of a condition on the pressure field for matrix consistency which was not required as the perturbation field matrices are not singular due to the Helmholtzianstyle inclusion of the zderivative component along the diagonal.  Detected an incorrect elemental vector product operation in L2 routine, which is now fixed.  Generalised the axisymmetric swirling flow solver to 2D Cartesian flows with nonzero w velocity fields. This will be used for Floquet analysis of vortex interaction studies where the vortices have nonzero axial flow in the zdirection. 17 NOVEMBER 2006:  Fixed predefined preprocessor symbol declarations for Itanium (APAC) processors.  Cleaned up some miscellaneous routines & messy statements throughout code. 13 NOVEMBER 2006:  Detected and fixed a bug which had corrupted the 2nddimension elemental derivative matrix in 3D only. 12 NOVEMBER 2006:  In "main.f90", VIPER is now recognized as "Version 3", reflecting the recent implementation of the optional scalar transport by advectiondiffusion.  Implemented a loworder scalar advectiondiffusion scheme. Scheme uses a 2ndorder predictorcorrector scheme for advection of the auxiliary equation used to provide the scalar field at the "departure point" of the Lagrangian discretization of the advectiondiffusion equation. The Lagrangian form of the transport equation is a simple diffusion equation, which is solved using a firstorder implicit scheme. A variable number of advection steps per diffusion update are permitted. 9 NOVEMBER 2006:  Detected a bug (through IA64 machine runtime errors on APAC) in the sparse matrix factorization routine. Problem caused by indefinite Laplacian matrices. Have now altered the routines to solve an unsymmetric matrix with a single nonzero entry in an extra row, rather than using the previous full extra row & column of ones. Should provide higher accuracy and avoid runtime errors. 8 NOVEMBER 2006:  Ported code over to Intel Fortran 9.1 on Windows IA32 machines (previously Lahey Fortran Express). Currently having trouble using the TECIO DLL library. Other aspects of the solver appear to work correctly. Minor array bounds errors were detected during the migration. 7 NOVEMBER 2006:  Detected an error in which program exits with untraceable EXCEPTION_ACCESS_VIOLATION error on a Windows IA32 testbed. This occurs regardless of Intel MKL version used, indicating that the Lahey Fortran compiler might be at fault. Tests are underway to identify the source of the error, but this is problematic as the error has no easily identifiable pattern. Attempting to install Intel Fortran 9.1 compiler to crosscheck. 6 NOVEMBER 2006:  Added the ability to impose uniform pressure gradients (in x, y & zdirections) via the PGRAD command. The pressure gradients are imposed during the advection step, and are also included in the estimate of the highorder homogeneous pressure boundary condition. This facilitates an easy method for computing pressuredriven periodic flows. 4 NOVEMBER 2006:  Removed obsolete routines which provided RungeKutta stepping for the initial 2 time steps  now exclusively employing 3rdorder backwards multistep time stepping.  Modified SAVE and LOAD routines to work with velocity fields over previous 3 time steps, instead of only at current time. This avoids the annoying perturbation that was added when simulations were restart from saved files due to the solver estimating the previous velocity fields for the backwardsmultistep time integration. 30 OCTOBER 2006:  Fixed bug in TEC_BIN routine, where gradient quantities were incorrect due to using the wrong numbering map.  Tightened code in static condensation routines: some redundant code remained from recent boundary numbering restructuring.  The unique global node numbering for each variable means that implementation of future variables such as a scalar field is simpler, and no convoluted remapping is required in the computations.  Completed implementation of reorganization/procedurization of boundary condition allocation and node renumbering. Still some code to tidy up  no need to shuffle between base mesh numbering & reduced numbering when periodic boundaries are present. This is now intrinsic to the number maps. Extensive testing required to ensure no "global_number_?" or "bmap_?" indexing matrices are out of place. 25 OCTOBER 2006:  Began implementation of scalar advectiondiffusion field implementation. 24 OCTOBER 2006:  Implemented userdefined static and transient Dirichlet pressure boundaries.  Replaced backwards integration estimates of initial 3D velocity fields with a direct copy of current time, as previous method was too unstable.  Fixed another bug in intermesh reinterpolation for LOAD routine.  Fixed a bug in the polynomial order reinterpolation routine by reducing ALLOCATE calls. 23 OCTOBER 2006:  A bug yet to be fixed: diverged solutions develop from loaded (interpolated?) 3D fields.  Fixed another bug in intermesh reinterpolation for LOAD routine.  Fixed a bug in the polynomial order reinterpolation routine by reducing ALLOCATE calls. 20 OCTOBER 2006:  Finished crossmesh interpolation feature of LOAD routine in 2D  3D still to be finalized. 18 OCTOBER 2006:  Partial implementation of an interpolation feature of the LOAD command which allows loading of data from a file generated from a different mesh  the data is interpolated onto the new mesh providing the file was saved with the "m" option. Still need to make mapping derivative calculations portable.  Added a "m" option to SAVE and LOAD routines  this option saves or loads the vector field by interpolating the old data and old coordinates onto the new mesh (as per the configuration file). 9 OCTOBER 2006:  Tweaked screen output so that numbers display more nicely during config & initialization.  Fixed file sequencing so that SAVE or TECP calls dumping different Floquet modes are independently sequenced. 6 OCTOBER 2006:  Added a reinterpolation feature to the LOAD command to permit the loading of solutions with a different number of quadrature points. 19 SEPTEMBER 2006:  Fixed a bug in the TRACK SEED routine, where particles were placed at +ve coordinates only, not over whole domain. 18 SEPTEMBER 2006:  Found & fixed an annoying bug in the Itanium compilation of the io.f90 module. "ifort" did not like a WRITE(buffer,*) call, where "buffer" was a CHARACTER string.  Obseleted "gvar_monitor" and replaced with runtime command MONITOR, which works the same way, but allows for multiple simultaneous point velocity monitoring into numerous filenames.  Modified "TRACK SEED" routine so that particle distribution performed in physical space. 17 SEPTEMBER 2006:  Fixed a bug in LOAD routine  perturbation fields were not being read from the correct position. 16 SEPTEMBER 2006:  Fixed a bug in LOAD routine  actual vector fields were not being retrieved for perturbation fields.  Fixed a bug where the SAVE routine was not defaulting to the "k=0" base flow mode on a SAVE call.  Removed unnecessary OPTIONAL specifiers for some parameters passed to routines which execute SAVE and LOAD commands  makes for neater code. 14 SEPTEMBER 2006:  Added "f" option for filename selection for LOAD routine, and added "k" option to both SAVE and LOAD routines to allow Floquet analysis perturbation fields to be stored and retrieved as well as base flow fields.  Added optional file name selection for time history monitoring. Useful for monitoring the time histories of several simulations in the one directory.  Fixed an error where an ALLOCATABLE array in the particle injector locator routine was not being DEALLOCATED. 13 SEPTEMBER 2006:  Fixed a bug in the particle tracking routine where injector points which lay near an element boundary were occasionally being missed as the search for the elemental coordinates of the injector location only searched the first element found which contained the nearest global node to the injector location. If the node is on an edge, face, or corner of an element, several elements need to be tested to find the actual location.  Fixed a bug in the userspecified variables facility in which runtime errors were encountered when no userspecified variables were defined. 7 SEPTEMBER 2006:  Added a new command "INT", which performs an integral over the computational domain of a user specified function. The function can include time, spatial variables, velocities and their spatial gradients, the Reynolds number, and any userdefined variables from the configuration file. 5 SEPTEMBER 2006:  Added an option for SAVE and TECP routines which adds a sequential number string to the output filenames to facilitate compact macro loops when collecting large series of data files for animation, etc. 31 AUGUST 2006:  Added a feature to the configuration file "gvar_usrvar", which defines a userspecified variable for which a supplied function is evaluated. 19 AUGUST 2006:  Fixed Gaussian blur of particle densities in Tecplot routine  have now implemented a correct expression compensating for the circular/spherical distributions in 2D/3D. The integrals of these functions have been verified to be unity in each case. 16 JULY 2006:  Combined Newtonian and nonNewtonian solvers for consistency. NonNewtionian computations are invoked whenever a nonlinear viscosity is entered in the "viper.cfg" file through the "gvar_nnvisc" function.  Added an unmissable warning message to the nonNewtonian solver to clearly identify when zero or negative viscosities are computed, which invariably cause simulation instability. 29 JUNE 2006:  Added userdefined filename functionality to output of Floquet multipliers.  Altered header of "flowrate.dat" files so that the boundaries are numbered "bndry1", "bndry2", etc., rather than simply "1", "2", etc. This allows the files to be input directly into Tecplot, preserving correct columns. 24 JUNE 2006:  Resolved an issue where restarting from a saved axisymmetric flow field was impossible due to incorrect treatment of the diffusion terms during prediction of previous time step velocity fields.  Fixed problem with advection of axisymmetric flows, tested on flow past a sphere, and now predicting correct drag forces and Floquet mode stability. 23 JUNE 2006:  Detected errors in rotational and skewsymmetric forms of advection term in cylindrical coordinates. This has caused an effective reduction in Reynolds number for flow past a sphere.  Disabled rotational form of acceleration terms for axisymmetry. 18 JUNE 2006:  Added a function "FREEZE", which cessates time integration of the base flow. This reduces the cost of steadystate Floquet stability analysis or particle tracking.  2D Cartesian Floquet linear stability analysis implemented, and tested on a circular cylinder wake  successfully predicted the emergence of Mode A instability. 16 JUNE 2006:  Fixed bug in 3D code which resulted in scrambled meshes following recent "%n()" alteration.  Improved error trapping to accommodate computations with 1storder elements (no interior nodes). 13 JUNE 2006:  Implemented advection step for Floquet analysis perturbation fields.  Modified "max du" reporting during time integration to include perturbation field maximum velocity change. 6 JUNE 2006:  Began implementing Floquet linear stability analysis for 2D and axisymmetric solvers.  Added "gvar_?" commands to VIPER "HELP" facility.  Implemented a facility for setting a userdefined initial velocity field in "viper.cfg". 30 MAY 2006:  Replaced "%n1, %n2, ..." and "%b1, %b2, ..." node number & boundary type identifiers with arrays, allowing some reduction of loop sizes.  Fixed enforcement of periodic boundaries in axisymmetric computations with swirl. 28 MAY 2006:  Increased precision of "FLOWRATE", "FORCES" and "L2" routine output to 18 significant figures, and added "t" variable to "FLOWRATE". 22 MAY 2006:  Improved functionality of "FORCES" routine  now permits user to specify a file name to save to, in a manner aligned with functionality of the "FLOWRATE" routine. 19 MAY 2006:  Added spatial coordinate variables to function for nonNewtonian viscosity.  Repaired nonNewtonian solver to align with current Newtonian solver. 3 MAY 2006:  Implemented exact periodic velocity boundary condition (periodic nodes only counted once instead of inexact averaging technique previously used).  Consolidated redundant code in FLOWRATE, FORCES modules, as well as compressed Cartesian and axisymmetric diffusion substep routines into one module. Compile time reduced by 75% and binaries approx 10% smaller.  Consolidated redundant code in symmetry boundary correction routines. 2 MAY 2006:  Consolidated redundant code in "make_bmap" and "make_bmap_3d" routines so that both 2D and 3D are computed using "make_bmap" routine, ensuring consistency in boundary implementation. 26 APRIL 2006:  Fixed problem with 3D "forces" routine  the viscous terms were being dotted with incorrect normal vectors (always normal to 1st face, not correct face). 25 APRIL 2006 (ANZAC day):  Tests showed that pressure BC was being subtracted instead of added  swapped this around with improvement in mass conservation & presumably temporal accuracy.  Important! Need to check the sign of the pressure BC sfc integral in the pressure substep  this might now be negative due to correction of sign of mass matrix elements.  Fixed bug in Tecplot output routine where compressible vectors were being allocated for incompressible 2D flows, causing a crash upon subsequent calls to "tecp". 23 APRIL 2006:  Coded up global static condensation solver for RungeKutta vectors for compressible solver. Solver not yet operational  boundary conditions not implemented yet. 22 APRIL 2006:  Found some errors in the construction of compressible flow matrices, but still results in di follows: (p,q,r) > (vertical, horizontal, height) > (xi2, xi1, xi3) 18 APRIL 2006:  Implementing compressible flow solver following recent papers by J. Iannelli. Solver uses a diagonally implicit 2ndorder RungeKutta algorithm to compute compressible NavierStokes equations modified to incorporate upwinding in the differential equations being solved by means of an "acousticconvective upstream resolution algorithm". Code compiles but boundary conditions not yet implemented. 10 APRIL 2006:  Modified the Tecplot data output routine to compute 3D quantities on 2D mesh for Axisymmetric computations with swirl.  Implmeneted axisymmetric computations with swirl (nonzero wvelocity evolved with zdirection gradients set to zero.  AXI toggle command changed to a cycling command, allowing selection of three 2D modes: 2D Cartesian, Axisymmetric without swirl, and axisymmetric with swirl. 9 APRIL 2006:  Axisymmetric version of 2D solver implemented using cylindrical coordinates. Formulation as per Blackburn & Sherwin (J Comp Phys, 2004). Axisymmetry invoked with "AXI" command, and employs the xaxis as the axis of symmetry, with y being the radial direction. 8 APRIL 2006:  Extended periodic boundaries to 3D  still xdirection only. 7 APRIL 2006:  Rewrite of boundary definition code successful  new "btag" format now required in "viper.cfg" files.  Planning to redesign boundary definitions in viper.cfg file: user specifies 2digit type code for each boundary number, with 1st & 2nd digits defining velocity & pressure conditions, respectively. Bndry code numbers 1, 2, 3, 4 & 5 are fixed and userdefined static and transient Dirichlet boundaries, periodic and symmetry boundaries, respectively.  Added periodic velocity boundary condition (restricted to 2D, xdir only at this stage).  Added pressure "p" as a variable for transient userdefined boundary functions. 5 APRIL 2006:  APAC simulations reveal that the current version of the code has greatly improved temporal characteristics on an initialconditionindependent computation: Testing the temporal convergence of the shedding period of a cylinder wake.  Replaced CONSERVE command with ADVECT, which now allows three options for the form of the advection operator: Convective, rotational and skewsymmetric. Skewsymmetric is now the default as it conserves linear momentum and kinetic energy in the inviscid limit, and it introduces minimal aliasing errors. 3 APRIL 2006:  Further refined the displaying of infomation to the user as VIPER loads and initialises.  Fixed bug in rotational form of the advection operator (employed after a CONSERVE command). 1 APRIL 2006:  Cleaned up configuration and initialisation reporting to screen.  Implemented a fancier header logo displayed upon program invocation. 31 MARCH 2006:  Still a problem with temporal convergence tests based on point velocities, etc in the flow. New tests being performed based on frequency measurements taken from time history traces of a Karman shedding wake.  Added a "L2 norm" functionality, where an integral of the velocity magnitude over the computational domain is computed. 28 MARCH 2006:  Careful inspection of variation of flow quantities over the first few time steps revealled that much of the temporal order issues were due to an effectively 1storder initial step due to the incorrect previous time step velocity fields. Two virtual velocity fields at times t0dt and t02dt have been constructed using an RK4 backwards time integration of the advection and diffusion parts of the NavierStokes equations. New temporal accuracy results to follow. 26 MARCH 2006:  Tests showed that pressure Neumann BC being incorrectly applied  the gradients were negative of what they were intended to be. With correct sign, solution still only first order. 24 MARCH 2006:  Problems detected with normal boundary vector construction  had become incorrect as a result of Dxi1 & Dxi2 matrices being defined in wrong directions  this also affected forces/flowrate calculations.  Found error in pressure substep  was incorrectly imposing Dirichlet velocity boundary conditions during intermediate update of velocity field  this might be the cause of the mysterious persisting firstorder temporal convergence of velocity despite 3rdorder time integration.  Implemented and tested 3D particle tracking  results appear promising  multielement simulations correctly tracking across elements.  Cleaned up code in symmetry boundary condition module  compilation time extremely slow in here, so hopefully this will help. 21 MARCH 2006:  Added particle tracking functionality  can now switch off injection of particles midcomputation.  Modified distribution variance in Tecplot data file output particle density variable  now set depending on local density of sample points  the finer the mesh, the lower the variance. This should produce more quality in regions of interest. 20 MARCH 2006:  Added a Tecplot output variable "particles", which plots a sum of a normal Gaussian distribution of the proximity of particles to each data point in the plot. Currently the standard distribution (diffusion) of the particles is fixed at 0.05 length units.  Fixed a bug in Tecplot dumping routine where extra data was being added due to old number of nodes being passed to TECIO routines after cleanup and reduction of duplicate nodes.  Implemented 2D particle tracking, and laid the code base for 3D (just need to code up hexahedral element face adjacency information). 16 MARCH 2006:  Moved looping in "step" command to within the stepping subroutine.  Implemented a 4thorder RungeKutta scheme to advance the advection term for the first three time steps, to accurately fill the previous step velocity vectors required for the 3rdorder backwards multistep scheme.  Fixed a small indexing bug in pressure boundary condition evaluation (could this be the 1storder issue?). 15 MARCH 2006:  Reorganised allocation, initialisation, and setting or RHS vector routines for time stepping so that the save/load routines function correctly. 13 MARCH 2006:  Fixed a bug which resulted in singular global Laplacian matrices when no Dirichlet pressure boundaries were present.  Added a function "chref", which adjusts the nonDirichlet velocities to simulate a change in reference frame motion (e.g. a body coming to rest, or accelerating). 12 MARCH 2006:  Implemented circular arcbased curvature algorithm for 2D elements: still need to implement continuous curvature around closed curves. 9 MARCH 2006:  Implemented some minor changes to pressure substep, which should slightly increase speed by reducing number of conditional statements in loops when evaluating pressure Neumann boundary condition.  Further tests show convergence still 1storder in time... where is the frakking problem?  Problem with pressure boundary condition: This Neumann condition was also being "enforced" on Dirichlet pressure boundaries (actually slightly altering the Dirichlet pressure value on the RHS of the equations). This might be the reason for the suboptimal temporal convergence often observed (convergence often little better than 1storder rather than 3rdorder). 8 MARCH 2006:  Successfully implemented a 3D curvature procedure based on blended circular arc segments. This produces a very natural looking curve, and importantly, reduces to perfect circles when one is being represented in the mesh. Tests show that a shape with surface area equal to a circle is described with 8 N=10 elements around the circumference, to the limit of numerical precision. 6 MARCH 2006:  Decided to change the element curvature algorithm so that it is based on computed circular arc segments rather than polynomial segments. Formulating method now, to be implemented shortly  should get better accuracy when computing flow through circular pipes or past cylinders. Was getting flowrates for pipes off by 1% even with 8 elements around circular crosssection!  Changed code so Dirichlet pressure boundaries are also enforced along edges of 3D elements which border a Dirichlet velocity region. This way the boundary is more accurately represented. 23 FEBRUARY 2006:  10% improvement in time stepping speed through use of global pointer storage for time step subroutines, as well as pointer reassignment as opposed to vector copies for flow vectors. 20 FEBRUARY 2006:  Replaced some FORALL statements containing vector notation, which the Intel Compiler is not optimising correctly, with DO loops. 13 FEBRUARY 2006:  By predicting the final CSR vector lengths prior to building them, was able to elimiate many "reallocate_csr" calls, resulting in a slightly reduced memory overhead, and a drastically improved initialisation time (50% improvement measured).  Added a "trim_csr" routine to "mat_ops.f90" which trims off the unneeded extra elements at the end of the CSR format column and value vectors. 12 FEBRUARY 2006:  Attempted a speedup of global Laplacian & Helmholtzian Schur complement matrices. Only 1% or 2% improvement. 8 FEBRUARY 2006:  Altered 3D curvature routine to permit separate curvature of differently numbered boundaries (e.g. better for branches in vascular systems  less chance of developing invalid elements).  Fixed a bug where 3D Dirichlet pressure boundaries were being replaced by interior boundary types along an edge. This was leading to slight errors in computation of pressuredriven flows on some meshes. 25 JANUARY 2006:  Isolated issue with 64bit Itanium version of 3D code incorrectly evaluating derivatives. Was due to vector notation in a WHERE construct within a FORALL loop. Replaced with another variable and now works.  With high levels of optimisation the code crashes between "make_bmap" and "make_global_number" routines. Attempts to identify the cause of this are unsuccessful  likely either a compiler bug or a problem with the external libraries. 24 JANUARY 2006:  Stripped out all unused routines in "mat_ops.f90", and called previously INTERFACEd routines directly. Code now more streamlined, and have removed unused userdefined types from "typeconst.f90"  Fixed an issue with the 3D solver's load/save routines. It was saving 2D fields due to an incorrect flag setting in "mesh.f90". 20 JANUARY 2006:  Increased precision of "lambda2" calculation in "tec_out.f90" routine, as intermediate steps can involve extremely large numbers in magnitude.  Fixed bug in "make_bmap_3d" which related to an incorrect indexing of the Dirichlet pressure boundary condition. 19 JANUARY 2006:  Reverted to solenoidal component of diffusion only in the highorder pressure boundary condition. The explicit treatment of the irrotational part created instabilities which were especially apparent for pressuredriven flows. 18 JANUARY 2006:  For lowReynolds number confined flows, an error of up to several percent was detected in mass conservation. This error has been reduced by an order of magnitude by reintroducing the velocity divergence component of the diffusion term in the highorder pressure boundary condition. This is the complete form of the term, and does not require a divergencefree field to be valid. 14 JANUARY 2006:  Added time derivative term to highorder pressure boundary condition. Improves accuracy of timevarying boundaries.  Fixed bug in viscous component of drag force routines in 2D & 3D. Terms were ommitted from the shear stress calculation. Tested on circular cylinder wake & works. 3 JANUARY 2006:  Moved the nonNewtonian nonlinear diffusion explicit step to before the pressure correction, ensuring that the incompressibility condition is satisfied in the same manner as in the Newtonian solver. 31 DECEMBER 2005:  Removed the last "TYPE(vector)" statement from the "tec_out" module. 1531 DECEMBER 2005:  Replaced 3rdorder AdamsBashforth advection / CrankNicolson with theta mod diffusion with 3rdorder stifflystable backwards multistep scheme. Testing promising, but issue detected at higher numbers of nodes per element  some edge boundary nodes develop a wierd pressure value which perturbs solution. 14 DECEMBER 2005:  Fixed error in surface integral determination of pressure boundary condition. Now have 2ndorder convergence of velocity fields, but pressure convergence from 1 to 0th order as time step decreases. 13 DECEMBER 2005:  Fixed small bug in "forces.f90" 2D routine, which arose after Newtonian & nonNewtonian solvers were amalgamated.  Fixed issue with pressure BC (there was a ve not +ve vorticity in the 2D formulation. Computations now slightly more stable. Consistency as time step reduced needs to be checked. 10 DECEMBER 2005:  Altered global numbering so that fixed Dirichlet boundaries take precedence over other boundary types, especially symmetry boundaries.  Altered "save" and "load" functions to store fields elementally. This way the boundary types, etc can be changed between loadings (which changes global numbering) without scrambling flow field data. 8 DECEMBER 2005:  Fixed bug in 2D "forces" routine for nonNewtonian computations  shear rates now taken from nonlinear viscosity. 6 DECEMBER 2005:  Implemented a 3D version of the nonNewtonian solver (not yet tested).  Ironed some wrinkles out of nonNewtonian version of code  small errors in shear rate determination and employment of linear reference viscosity. Stability and physical appearance of solutions improved.  Employed a runtime parsing of relationship for nonlinear viscosity as a function of shear rate.  Added 2D & 3D shear rate variables to Tecplot binary dumps. 3 DECEMBER 2005:  Reorganised time integration into separate modules  the goal is to be able to switch integration schemes at compile time rather than recode the routines.  Implemented a nonNewtonian time integration scheme, which splits the viscous term into a nonlinear part and a linear part. Tests are currently underway. 30 NOVEMBER 2005:  After testing, derivatives, integrals, 2D & 3D sims with all boundary types working.  Fixed bug in boundary type categorisation routine  was failing when a userdefined boundary was listed prior to a fixed Dirichlet boundary.  Fixed bugs in the 3D bmap & Jacobian routines which were due either to typos in reference texts or from loop optimisations I had implemented.  Included an alternative time integration module, "time_int_blood.f90", which will be used to facilitate nonNewtonian fluid modeling. 29 NOVEMBER 2005:  Fixed a small bug in tec_bin routine to avoid interpolation errors when the interpolation point corresponds to a data point.  Massive speedup to GLL quadrature point evaluation due to more clever recursive evaluation of Jacobi polynomial. Now almost instantaneous. Also removed unnecessary routines in gll.f90 file. 23 NOVEMBER 2005:  50% speedup of initialisation phase, 26% speedup of time integration thanks to reducing unnecessary code and adding new sparse BLAS commands provided in the Intel MKL 8.0. 2 NOVEMBER 2005:  Replaced many intrinsic MATMUL calls with BLAS equivalents  a sizeable performance improvement. 26 OCTOBER 2005:  Formalized "slipwall" bndry condition to enforce both the tangential flow and zero tangent vorticity. This boundary condition has been observed to function well in both 2D and 3D.  Included tangent vectors in "nml_vect" module, which are employed in "slipwall" boundary calculations.  Assigned "INOUT" INTENT to "p_global" pressure vector in pressure substep routines to avoid crashes detected with Dirichlet pressure boundary conditions. 2 OCTOBER 2005:  Implemented "symmetry" or "slipwall" (zero normal velocity) boundary condition (number 4).  Set up routine to precompute normal vectors out of each boundary to speed up time integration. 30 SEPTEMBER 2005:  Fixed bugs with 3D "tec_bin" and time integration routines.  Implemented untested lambda_2 data field in "tec_out.f90" routine, in both 2D and 3D. 28 SEPTEMBER 2005:  Using full storage for all Laplacian & Helmholtzian matrices (except Schur complement) > much faster initialisation and time stepping. 27 SEPTEMBER 2005:  Regressed to a REAL(DP) pointer array type for velocity/pressure vectors in "time_int.f90". 26 SEPTEMBER 2005:  Attempted more speedups with no success. 25 SEPTEMBER 2005:  Simplified vector generation in "tec_bin" routine.  Approx. 50% speedup by using CSR format derivative matrices for matrix multiplies over CSC format in time integration.  Slight speedup by swapping index order in "bmap", "global_number" arrays. 23 SEPTEMBER 2005:  Speedup optimisations to code performed throughout "time_int.f90". Approx. 35%40% increase in speed.  PARDISO solve calls now in "time_int.f90" routines for efficiency (approx 5% better). 22 SEPTEMBER 2005:  Added variable filename functionality to "flowrate" routine. 20 SEPTEMBER 2005:  Implemented 2D & 3D static Dirichlet pressure boundary condition (with zero normal velocity gradients). This will be useful for modeling pressuredriven flows.  Rewrote "make_bmap" to conform with simpler "make_bmap_3d" routine: now significant code redundancy. 18 SEPTEMBER 2005:  Implemented accurate dp/dn boundary condition to ensure mass conservation is accurately enforced.  Added velocity magnitude data set "vel_mag" to Tecplot output files. 14 SEPTEMBER 2005:  Fixed "init" so that solutions can be reinitialised successively.  Tried a "tecp" speedup to no success.  Implemented toggle between convective and rotational forms for acceleration terms.  Identified nonsmooth boundaries (i.e. corners) as the culprit for inaccuracy in viscous computations. 13 SEPTEMBER 2005:  Rewrote diffusion routine: still haven't found why mass not conserved in branched meshes. 8 SEPTEMBER 2005:  Rewrote 3D "forces" routine  results appear more acceptable.  "flowrate.f90" produces incorrect results if compiled using "o2" option  compile using "o1".  3D flowrate implemented  testing incomplete.  Debugged 2D flowrate monitor routine. Now for 3D... 7 SEPTEMBER 2005:  Implementing 2D boundary flowrate routines. 2D routine near completion...  Altered DP doubleprecision definition to "KIND(1.0D0)" in "typeconst.f90", and tweaked size of "small" parameter in "tec_out.f90" to remove annoying artificial internal boundaries from Tecplot data files in 2D. 31 August 2005:  Sped up "tecp" routine by a factor of approximately 2.5 times. 30 August 2005:  Fixed problem with userdefined boundaries.  Detected problem with userdefined Dirichlet boundaries (showing up on reverse face of elements as well)...  Fixed bugs in facebiased blending component of interior node blending routine!  Detected bug in interior node location blending  partially rectified, but still buggy. 29 August 2005:  Removed problem with first global to local spatial coordinate vector transform which was causing 3D curvature to be discontinuous across element faces  3D curvature now working! 27 August 2005:  Multiface 3D curvature implemented  still need to improve smoothing across element edges.  Improved 3D curved face blending: Preserves edge curvature throughout face (good for curvature in a single direction). 26 August 2005:  Curvature (singleface) implemented. Bugs still present. 25 August 2005:  Created vectors to store element, face and boundary surface numbers for curvature  Simplified 3D element blending routines based on global indexing in readiness for 3D curvature.  Built global vertex, edge and face numbering for 3D curvature in "mesh.f90", routine "make_jacobians_3d"  Changed source code file extensions to standard ".f90" from ".f95" for conformance across platforms. 24 August 2005:  Fixed tec_out.f95 so that each element is not surrounded by its own boundary. Pre 24 August 2005:  Wrote code and made lots of changes.
Platforms: Available on Windows PC, and both serial and parallel Linux platforms
Floquet linear stability analysis for 2D Cartesian & axisymmetric simulations
Cartesian 2D/3D & axisymmetric computation of incompressible fluid flow
Automated curvature based on blended piecewise circular arc segments
Implements the efficient and scalable PARDISO package for matrix operations
Userdefined transient or steady boundary conditions parsed at run time
Provides point velocity/pressure monitoring
Viscous & pressure force calculations on boundaries
Boundary flow rate monitoring
Data output in Tecplot binary ".plt" format
Euler & viscous compressible flow formulation employing the ACURA method of Prof Joe Iannelli, City University, London, UK.
Turbulence modeling: Implementation of DetachedEddy Simulation method.
Viper facilitates both an Arnoldi method as well as a power method to determine the eigenvalues and eigenvectors of threedimensional instability modes on twodimensional base flows. Threedimensional reconstructions of the flow can be generated for plotting and visualisation, and the code provides the complex components of the Floquet multiplier  the amplification factor dictating the linear growth rate of each instability mode.
VIPER features axisymmetric (zr cylindrical coordinates) solver capabilities, both with and without swirl, in addition to Cartesian 2D & 3D solvers.
Simulations can be performed on twodimensional quadrilateral meshes, and threedimensional hexahedral meshes. A spectralelement/Fourier method is implemented to efficiently compute 3D flows in domains which are homogeneous in the third dimension.
2D computation of vascular flow in a segment of the interlobular arcade within the kidney.
2D computation of flow past a NACA
4412 aerofoil. Coloured contours reveal the vorticity field around
the wing, streamlines are shown in white, and the spectralelement
mesh is shown in grey.

Top: 3D flow in a straight pipe segment demonstrating the capability
of simulating pressuredriven flows.
Bottom: Shear rate contours for flow driven through a Tjunction from the bottom left. 
VIPER employs a novel automated mesh curvature algorithm, which automatically generates a smooth curved surface (or edge in 2D) based on blended circular arc segments. This method combines superb flexibility and generality in application, while defaulting to a circular geometry when one is desired  very useful for fundamental applications of the code.
This plot shows the exponential convergence of error in a numerical estimate of the circular crosssectional area of a mesh constructed with 8 spectral elements around the circle perimeter. Just 7 nodes in each elemental coordinate direction are sufficient to describe a circle accurate to 12 significant figures in this case!
The above sequence of images simulates laserinduced fluorescent dye visualization of the twodimensional wake behind a cylinder. The cylinder is initially at rest, and translates left for 10 time units at Reynolds number Re = 200, before being rapidly arrested. Observe how the wake vortices pair up with induced vortices due to the backwash over the cylinder, which then convect away from the cylinder in a curved trajectory due to the difference in circulation between each vortex in the pair.
Download an animation of the above sequence: [Large  18.9 MB] [Small  6.13 MB]
Particle tracking is performed by updating particle positions within elements using a 4thorder RungeKutta time integration scheme in parametric space, while a linear series of substeps is employed to step to and across element interfaces. Visualization of particles can be performed either by outputting the discrete particle locations in physical space, or by plotting the particle concentration as per the above image. The concentration is calculated based on a Gaussian distribution about each data point, with a variance calculated based on the local mesh refinement.
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