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A kinetic flux-vector splitting method for the shallow water magnetohydrodynamics


Qamar,  S.
Physical and Chemical Foundations of Process Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
COMSATS Institute of Information Technology, Islamabad, Pakistan;

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Qamar, S., & Mudasser, S. (2010). A kinetic flux-vector splitting method for the shallow water magnetohydrodynamics. Computer Physics Communications, 181(6), 1109-1122. doi:10.1016/j.cpc.2010.02.019.

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. © 2010 Elsevier B.V. All rights reserved. [accessed May 7,2010)