Numerical Study of the Discontinuous Galerkin Method for Solving the Baer–Nunziato Equations with Instantaneous Mechanical Relaxation

被引：0

作者：

R. R. Polekhina ^{[1
]}

E. B. Savenkov ^{[1
]}

机构：

[1] Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow

来源：

Mathematical Models and Computer Simulations | 2024年 / 16卷 / 6期

基金：

俄罗斯科学基金会;

关键词：

discontinuous Galerkin method; nonconservative scheme; shock waves; two-phase media;

D O I：

10.1134/S2070048224700583

中图分类号：

学科分类号：

摘要：

Abstract: This paper is a numerical study of the discontinuous Galerkin method for solving the two-phase Baer–Nunziato (BN) equations with instantaneous mechanical relaxation. From a mathematical point of view, the system of equations is a nonconservative hyperbolic system of equations. Unlike conservative hyperbolic systems of equations for which numerical methods are well known and developed, the numerical solution of nonconservative hyperbolic systems is a more complex problem that requires generalization of the Godunov method. The computational algorithm is based on solving the hyperbolic part by a second order discontinuous Galerkin method with path-conservative HLL or HLLEM numerical flows. To monotonize the solution, the WENO-S limiter is used, which is applied to the conservative variables of the model. To take into account relaxation processes, a new algorithm for instantaneous relaxation is proposed, within which the determination of equilibrium values of the velocity and thermodynamic variables is reduced to solving a system of algebraic equations. To test the proposed numerical algorithm, the results of numerical calculations are compared with known analytical solutions in one-dimensional formulations. To demonstrate the capabilities of the proposed algorithms, a spatially two-dimensional problem of the flow around a step is considered, as well as a two-phase version of the triple-point problem. The calculation results show that the proposed algorithm is robust and allows calculations for two-phase media with a density jump of ~1000. © Pleiades Publishing, Ltd. 2024.

引用

页码：826 / 842

页数：16

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