Well-Balanced Central Scheme for the System of MHD Equations with Gravitational Source Term (Communications in Computational Physics, 2022)
A well-balanced second order finite volume central scheme for the magnetohydrodynamic (MHD) equations with gravitational source term is developed in thispaper. 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 usingghost staggered cells. A subtraction technique is used on the conservative variableswith 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 afterapplying the constrained transport method (CTM) for unstaggered central schemes atthe 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 theliterature.