A well-balanced finite volume solver for the 2D shallow water magnetohydrodynamic equations with topography

In this paper, a second-order finite volume Non-Homogeneous Riemann Solver is used to obtain an approximate solution for the two-dimensional shallow water magnetohydrodynamic (SWMHD) equations considering non-flat bottom topography. We investigate the stability of a perturbed steady state, as well a...

Full description

Saved in:
Bibliographic Details
Published in:Computer physics communications 2024-12, Vol.305, p.109328, Article 109328
Main Authors: Cissé, Abou, Elmahi, Imad, Kissami, Imad, Ratnani, Ahmed
Format: Article
Language:English
Subjects:
Finite volume method
GLM method
Hyperbolic system
Stationary state
SWMHD equations
Topography
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a second-order finite volume Non-Homogeneous Riemann Solver is used to obtain an approximate solution for the two-dimensional shallow water magnetohydrodynamic (SWMHD) equations considering non-flat bottom topography. We investigate the stability of a perturbed steady state, as well as the stability of energy in these equations after a perturbation of a steady state using a dispersive analysis. To address the elliptic constraint ∇⋅hB=0, the GLM (Generalized Lagrange Multiplier) method designed specifically for finite volume schemes, is used. The proposed solver is implemented on unstructured meshes and verifies the exact conservation property. Several numerical results are presented to validate the high accuracy of our schemes, the well-balanced, and the ability to resolve smooth and discontinuous solutions. The developed finite volume Non-Homogeneous Riemann Solver and the GLM method offer a reliable approach for solving the SWMHD equations, preserving numerical and physical equilibrium, and ensuring stability in the presence of perturbations.
ISSN:0010-4655
DOI:10.1016/j.cpc.2024.109328