Abstract
AbstractWe propose a second-order accurate semi-implicit and well-balanced finite volume scheme for the equations of ideal magnetohydrodynamics including gravitational source terms. The scheme treats all terms associated with the acoustic pressure implicitly while keeping the remaining terms part of the explicit sub-system. This semi-implicit approach makes the method particularly well suited for problems in the low Mach regime. We combine the semi-implicit scheme with the deviation well-balancing technique and prove that it maintains equilibrium solutions for the magnetohydrostatic case up to rounding errors. In order to preserve the divergence-free property of the magnetic field enforced by the solenoidal constraint, we incorporate a constrained transport method in the semi-implicit framework. Second order of accuracy is achieved by means of a standard spatial reconstruction technique with total variation diminishing property, and by an asymptotic preserving time stepping algorithm built upon the implicit-explicit Runge–Kutta time integrators. Numerical tests in the low Mach regime and near magnetohydrostatic equilibria support the low Mach and well-balanced properties of the numerical method.
Funder
Deutsche Forschungsgemeinschaft
Fondazione Cariplo
Ministero dell’Università e della Ricerca
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
1 articles.
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