An Energy Stable Local Discontinuous Galerkin Method for a Binary Compressible Flow
Year: 2025
Author: Hui Sun, Lulu Tian, Hui Guo
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 888–908
Abstract
This paper focuses on an energy-stable local discontinuous Galerkin (LDG) method for a binary compressible flow model. Since the densities and the momentum are highly coupled in the equations, and the test and basis functions in LDG discretizations have to be in the same finite element space, it is difficult to obtain stable LDG discretizations for the binary compressible flow model. To tackle this issue, we take the mass average velocity v and its square as auxiliary variables. These auxiliary variables are chosen in the stability analysis as the test functions for the momentum and density balance equations, respectively. Using the Crank-Nicolson (CN) time integration method, we can prove then the stability of the LDG-CN discretization. Computations are provided to demonstrate the accuracy, efficiency and capabilities of the numerical method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0326
Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 3 : pp. 888–908
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Binary compressible flow energy-stable local discontinuous Galerkin method Crank-Nicolson time integration method.
Author Details
Hui Sun Email
Lulu Tian Email
Hui Guo Email