Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term

Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term

Year:    2022

Author:    Farah Kanbar, Rony Touma, Christian Klingenberg

Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 878–898

Abstract

A well-balanced second order finite volume central scheme for the magnetohydrodynamic (MHD) equations with gravitational source term is developed in this paper. The scheme is an unstaggered central scheme that evolves the numerical solution on a single grid and avoids solving Riemann problems at the cell interfaces using ghost staggered cells. A subtraction technique is used on the conservative variables with the support of a known steady state in order to manifest the well-balanced property of the scheme. The divergence-free constraint of the magnetic field is satisfied after applying the constrained transport method (CTM) for unstaggered central schemes at the end of each time-step by correcting the components of the magnetic field. The robustness of the proposed scheme is verified on a list of numerical test cases from the literature.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2022-0067

Communications in Computational Physics, Vol. 32 (2022), Iss. 3 : pp. 878–898

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    MHD equations unstaggered central schemes well-balanced schemes steady states divergence-free constraint constrained transport method.

Author Details

Farah Kanbar

Rony Touma

Christian Klingenberg

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