05-17
Application of Space-Time CE/SE Method to Shallow Water Magnetohydrodynamics Equations
Preprint series: 05-17, Preprints
The paper is published: This article will appear in the Journal of Computational and Applied Mathematics (JCAM).
- MSC:
- 76W05 Magnetohydrodynamics and electrohydrodynamics
- 76W05 Magnetohydrodynamics and electrohydrodynamics
- 35L65 Conservation laws
- 65M06 Finite difference methods
- 35L45 Initial value problems for hyperbolic systems of first-order PDE
- 35L67 Shocks and singularities, See also {58C27, 76L05}
Abstract: In this article we apply a Space-Time Conservation Element and Solution Element (CE/SE) method for the approximate solution of shallow water magnetohydrodynamics (SMHD) equations in one and two space dimensions. These equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two-dimensional with magnetic equilibrium in the third direction. In this article we are using a variant of the CE/SE method developed by Zhang, Yu and Chang (JCP-175, 2002). This method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions, respectively. In this method, a single conservation element at each grid point is employed for solving conservation laws no matter in one, two, and three space dimensions. The present scheme use the conservation element to calculate flow variables only, while the gradients of flow variables are calculated by central differencing reconstruction procedure. We give both one- and two-dimensional test computations. A qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution Galerkin schemes. The one- and two-dimensional computations reported in this paper demonstrate the remarkable versatility of the present CE/SE scheme.
Keywords: Sallow water magnetohydrodynamic equations, CE/SE method, conservation laws, hyperbolic systems, discontinuous solutions.
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