An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics

被引：15

作者：

Winters, Andrew R. ^{[1
]}

Gassner, Gregor J. ^{[1
]}

机构：

[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 67卷 / 02期

关键词：

Nonlinear hyperbolic conservation law; Nonlinear hyperbolic balance law; Shallow water magnetohydrodynamics; Finite volume; Entropy conservation; Entropy stability; NUMERICAL VISCOSITY; CONSERVATION-LAWS; SOLAR TACHOCLINE; SYSTEMS;

D O I：

10.1007/s10915-015-0092-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we design an entropy stable, finite volume approximation for the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that exactly preserves the entropy, which is also the total energy for the SWMHD equations. To guarantee the discrete conservation of entropy requires a special treatment of a consistent source term for the SWMHD equations. With the goal of solving problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.

引用

页码：514 / 539

页数：26

共 29 条

[1]

[Anonymous], 2002, FINITE VOLUME METHOD

[2] A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations [J].