Work

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

Year: 2026

Type: software-paper

Abstract: This paper introduces 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 on 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.itap.purdue.edu/DGFSproj/

Source: SoftwareX

DOI: 10.1016/j.softx.2026.102544

Authors: Evgeniia Vorozhbit, Brian Morton, Nirajan Adhikari, Alina A. Alexeenko, Jingwei Hu

Institutions: Purdue University West Lafayette, University of Washington

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: National Science Foundation