2D/3V Flux-reconstructed Discontinuous Galerkin Fast Spectral (DGFS)

is an open-source software code for solving single/multi-species Boltzmann equation and related kinetic models for gas flows. It is designed for CUDA-enabled GPUs and applies the high-order flux-reconstructed discontinuous Galerkin schemes. The primary codebase for the DGFS has been originally developed by Dr. Shashank Jaiswall as part of his PhD dissertation research supported under the NSF award "CDS&E: Deterministic Evaluation of Kinetic Boltzmann equation with Spectral H/p/v Accuracy".

The Boltzmann equation for gas flows describes the evolution of the gas molecular velocity distribution function $f = f(t,\boldsymbol{x},\boldsymbol{v})$ :

$\partial_t f + \boldsymbol{v\cdot \nabla_x}f = Q(f,f_*), \quad t >0, ~~\boldsymbol{x} \in \Omega \subset \mathbb{R}^3, ~~\boldsymbol{v} \in \mathbb{R}^3$

The collision integral calculations use two methodologies:

the explicit fast spectral schemes for full Boltzmann [Gamba 2017, Jaiswal 2019a, Jaiswal 2019b]. The method applies to general collision kernels, and the results can be "directly" compared with the DSMC without need of any recalibration or parametric fitting.
the implicit schemes for linear kinetic models [Dimarco 2013, Dimarco 2017]

The time integration is performed via:

1st/2nd order explicit Strong Stability Preserving (SSP) Runge Kutta (RK) schemes
1st/2nd/3rd order implicit-explicit Ascher-Ruuth-Spiteri (ARS) and backward-difference (BDF) schemes

The overall schemes are simple from mathematical and implementation perspective; highly accurate in both physical and velocity spaces as well as time; robust, i.e. applicable for general geometry and spatial mesh; exhibits nearly linear parallel scaling; and directly applies to general collision kernels needed for high fidelity flow modelling.

Requirements:

System Requirements: • Linux OS (Ubuntu, CentOS, etc.) • GCC ≥ 6.3.0 • OpenMPI ≥ 3.1.6 (with CUDA support recommended) • CUDA Toolkit ≥ 11.0 • Python 3.8+ • GMSH 2.15.0 (for mesh generation) • METIS (for mesh partitioning)

Python Dependencies (install via pip): • numpy • h5py • mpi4py • pycuda • gimmick==2.3 (must be pinned to 2.3 to avoid compatibility issues)

Installation Instructions

Create Working Directory

mkdir -p ~/DGFS
cd ~/DGFS

Install System Tools

Use your package manager or module system to install:

GCC (version ≥ 6.3.0)
OpenMPI (version ≥ 3.1.6 with CUDA support)
CUDA Toolkit (version ≥ 11.0)
make and cmake if not already installed

Example for Ubuntu:

sudo apt update
sudo apt install build-essential libopenmpi-dev openmpi-bin cmake

Download and install CUDA Toolkit from: https://developer.nvidia.com/cuda-downloads

Set Up Python Environment

Using venv:

python3 -m venv dgfs_env
source dgfs_env/bin/activate

Or using Anaconda:

conda create -n dgfs_env python=3.8
conda activate dgfs_env

Install Python Dependencies

pip install numpy h5py mpi4py pycuda
pip install --upgrade gimmick==2.3

Download DGFS-BE Solver

git clone https://github.itap.purdue.edu/DGFSproj/DGFS-BE-Solver.git
cd DGFS-BE-Solver

Install METIS

Using system package manager:

sudo apt install metis

Or install from source: http://glaros.dtc.umn.edu/gkhome/metis/metis/download

Install GMSH

Download and extract:

wget https://gmsh.info/bin/Linux/gmsh-2.15.0-Linux.tgz
tar -xzf gmsh-2.15.0-Linux.tgz

Define an alias:

echo "alias gmsh=~/DGFS/gmsh-2.15.0-Linux/bin/gmsh" >> ~/.bashrc
source ~/.bashrc

References:

[Gamba 2017] Gamba, I. M., Haack, J. R., Hauck, C. D., & Hu, J. (2017). A fast spectral method for the Boltzmann collision operator with general collision kernels. SIAM Journal on Scientific Computing, 39(4), B658-B674.
[Dimarco 2013] Dimarco, G., & Pareschi, L. (2013). Asymptotic preserving implicit-explicit Runge--Kutta methods for nonlinear kinetic equations. SIAM Journal on Numerical Analysis, 51(2), 1064-1087.
[Dimarco 2017] Dimarco, G., & Pareschi, L. (2017). Implicit-explicit linear multistep methods for stiff kinetic equations. SIAM Journal on Numerical Analysis, 55(2), 664-690.
[Jaiswal 2019a] Jaiswal, S., Alexeenko, A. A., and Hu, J. (2019) A discontinuous Galerkin fast spectral method for the full Boltzmann equation with general collision kernels. Journal of Computational Physics 378: 178-208. https://doi.org/10.1016/j.jcp.2018.11.001
[Jaiswal 2019b] Jaiswal, S., Alexeenko, A. A., and Hu, J. (2019) A discontinuous Galerkin fast spectral method for the multi-species full Boltzmann equation. Computer Methods in Applied Mechanics and Engineering 352: 56-84. https://doi.org/10.1016/j.cma.2019.04.015
[Jaiswal 2019d] Jaiswal, S., Pikus, A., Strongrich A., Sebastiao I. B., Hu, J., and Alexeenko, A. A. (2019) Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic context. Physics of Fluids 31(8): 082002. https://doi.org/10.1063/1.5108665

License:

DGFS is released as GNU GPLv2 open-source software. This code has been derived from "PyFR". Please see licenses folder for restrictions.

DGFSproj/DGFS-BE-Solver

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