SPECTER

SPECTER (Special Periodic Continuation Turbulence Solver) is a Fortran program (with some C bindings) that performs numerical integration in 3D space for a set of PDEs usually found in fluid dynamics.

A pseudo-spectral method is used to compute spatial derivatives, coupled with an adjustable order Runge-Kutta time stepping. When non-periodic directions are specified, SPECTER utilizes FC-Gram continuations to compute Fourier transforms with minimal overhead and considerable accuracy. At its present state, SPECTER has support for a single non-periodic direction. Support for two or more non-periodic directions is planned.

SPECTER is programmed to scale. It can be run in your workstation as well as in top notch supercomputers. With this in mind, the code is parallelized employing MPI, OpenMP and CUDA.

Note: CUDA support is currently experimental and not provided publicly yet. If you are interested in CUDA support please contact the author.

Getting SPECTER

If you have git installed in your system, you can run

git clone https://github.com/mfontanaar/SPECTER

Alternatively, you can fetch it using curl or wget with

curl/wget https://github.com/mfontanaar/SPECTER

If you are using a web browser, you can also get it via this link.

Prequisites

SPECTER needs Fortran and C compilers to be present in the system, and an installation of both FFTW 3.x and an MPI flavor (mpich, openmpi, etc.) is required. Additionally, for compiling with CUDA support the nVidia Cuda Compiler is needed.

Compiling

Compiling SPECTER is as simple as setting appropriate paths to the compilers, and the fftw and mpi libraries in the file src/Makefile.in. Parameters like simulation resolution, solver to employ, time-stepping order and floating-point precision can also be specified in the same file. The code is then compiled by running

make

while in the src/ directory. After running make, the output binary should be placed in the bin/ directory, and named like the chosen solver.

Running SPECTER

After the compilation, a binary file with the name of the selected solver is placed in bin/ directory. In that same directory, a file named parameter.inp can be found, where you can specify several important parameters like magnitude of the time step, the number of steps to perform, how often to save output information. Physical parameters like the forcing amplitude, the mmagnitude of the initial condition or the viscosity are also specified in bin/parameter.inp/. A full list of the parameters with their description can be found in the same file, as well as in src/README.md. After setting up parameters.inp you can run the code with

./SOLVER

If you are running SPECTER in a cluster that uses a queuing system like TORQUE or Slurm you must follow the instructions provided by the cluster administrator to add SOLVER to the queue.

Forcing and initial conditions

The expressions for the forcing fields and the initial conditions must be specified at compile time. They are defined in the files initialv.f90 or initialfv.f90 for the initial velocity field and the initial mechanical forcing, respectively. The same convention is used for the scalar or other fields. A set of commonly used forcings and initial conditions can be found in the src/examples/ directory.

Getting FC-Gram tables

For non-periodic directions, SPECTER uses tables to compute appropriate periodic extensions. A collection of commonly employed tables can be found in the tables/ directory. However, a supplementary Fortran program to generate these tables is available at https://github.com/mfontanaar/fctables.

More information

To get the best out of SPECTER we recommend reading the information provided in src/README.md for a detailed explanation of each compilation and runtime parameter.

References

• Fontana, M., Bruno, O. P., Mininni P. D. & Dmitruk P.; Fourier continuation method for incompressible fluids with boundaries. Comp. Phys. Comm. 256, 107482 (2020).DOI: 10.1016/j.cpc.2020.107482.
• Fontana M, Mininni PD, Bruno OP & Dmitruk P; Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions. Comp. Phys. Comm. 275, 108304 (2022). DOI: 10.1016/j.cpc.2022.108304.
• Bruno, O. P. & Lyon, M: High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements. Jour. Comp. Phys. 229, (2010). DOI: 10.1016/j.jcp.2009.11.020.
• Mininni P. D., Rosenberg D. L., Reddy R. & Pouquet A.; A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence. P. Comp. 37, 123 (2011). DOI: 10.1016/j.parco.2011.05.004.
• Rosenberg D. L., Mininni P. D., Reddy R. & Pouquet A.; GPU parallelization of a hybrid pseudospectral fluid turbulence framework using CUDA. Atmosphere 11, 178 (2020). DOI: 10.3390/atmos11020178.

Citation

If you use SPECTER for a publication, we kindly ask you to cite the following article: Fontana, M., Bruno, O. P., Mininni P. D. & Dmitruk P.; Fourier continuation method for incompressible fluids with boundaries. Comp. Phys. Comm. 256, 107482 (2020).DOI: 10.1016/j.cpc.2020.107482.

Depending on the solver, we also ask you to consider citing:

• MHD: Fontana M, Mininni PD, Bruno OP & Dmitruk P; Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions. Comp. Phys. Comm. 275, 108304 (2022). DOI: 10.1016/j.cpc.2022.108304.

Authors

• Mauro Fontana - Physics Department at University of Buenos Aires.
• Pablo D. Mininni - Physics Department at University of Buenos Aires.