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Volume 32, Issue 3
Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term

Farah Kanbar, Rony Touma & Christian Klingenberg

DOI: 10.4208/cicp.OA-2022-0067

Commun. Comput. Phys., 32 (2022), pp. 878-898.

Published online: 2022-09

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M08, 76M12, 65M22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-878, author = {Kanbar , FarahTouma , Rony and Klingenberg , Christian}, title = {Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0067}, url = {http://global-sci.org/intro/article_detail/cicp/21049.html} }
TY - JOUR T1 - Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term AU - Kanbar , Farah AU - Touma , Rony AU - Klingenberg , Christian JO - Communications in Computational Physics VL - 3 SP - 878 EP - 898 PY - 2022 DA - 2022/09 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0067 UR - https://global-sci.org/intro/article_detail/cicp/21049.html KW - MHD equations, unstaggered central schemes, well-balanced schemes, steady states, divergence-free constraint, constrained transport method. AB -

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.

Kanbar , FarahTouma , Rony and Klingenberg , Christian. (2022). Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term. Communications in Computational Physics. 32 (3). 878-898. doi:10.4208/cicp.OA-2022-0067
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