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 - <p style="text-align: justify;">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.</p>