Well-balanced central scheme for the system of MHD equations with gravitational source term. (English) Zbl 1496.65138
Summary: 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.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |
Keywords:
MHD equations; unstaggered central schemes; well-balanced schemes; steady states; divergence-free constraint; constrained transport methodReferences:
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