A kinetic flux-vector splitting method for the shallow water magnetohydrodynamics |
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Authors: | Shamsul Qamar Sidrah Mudasser |
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Affiliation: | a Department of Mathematics, COMSATS Institute of Information Technology, Park Road Chak Shahzad, Islamabad, Pakistan b Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany |
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Abstract: | A kinetic flux-vector splitting (KFVS) scheme for the shallow water magnetohydrodynamic (SWMHD) equations in one- and two-space dimensions is formulated and applied. These equations model the dynamics of a thin layer of nearly incompressible and electrically conducting fluids for which the evolution is nearly two-dimensional with magnetic equilibrium in the third direction. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the SWMHD equations. In two-space dimensions the scheme is derived in a usual dimensionally split manner; that is, the formulae for the fluxes can be used along each coordinate direction. The high-order resolution of the scheme is achieved by using a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Both one- and two-dimensional test computations are presented. For validation, the results of KFVS scheme are compared with those obtained from the space-time conservation element and solution element (CE/SE) method. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential in modeling SWMHD equations. |
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Keywords: | Shallow water magnetohydrodynamic equations Kinetic schemes MUSCL-type reconstruction Conservation laws Hyperbolic systems Discontinuous solutions |
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