DGFS-BE Solver: An open-source Discontinuous Galerkin Fast Spectral Solver for the full Boltzmann equation

This paper introduces the DGFS-BE solver, an open-source Discontinuous Galerkin Fast Spectral solver designed to address the complexities of the Boltzmann equation, a fundamental equation in kinetic theory. The solver combines the Discontinuous Galerkin method for spatial discretization with fast spectral methods for velocity discretization, offering high-order accuracy across various domains. Unlike traditional stochastic methods, DGFS adopts a deterministic approach, avoiding assumptions about the collision kernel and overcoming the limitations of the Direct Simulation Monte Carlo method in rarefied gas flow simulations. The solver’s integration with GPU CUDA technology ensures efficient computation, making it suitable for applications ranging from aerospace engineering to microscale flows. Several test cases, including Couette flow, Fourier conduction, normal shock waves, and pressure-driven microchannel flow, demonstrate the solver’s accuracy and performance. The solver is available at: https://github.com/DGFSproj/ .