Student Paper: Removal of pseudo-convergence in coplanar and near-coplanar Riemann problems of ideal magnetohydrodynamics solved using finite volume schemes

A.D. Kercher and R.S. Weigel

Numerical schemes for ideal magnetohydrodynamics (MHD) that are based on the standard finite volume method (FVM) exhibit pseudo-convergence in which irregular structures no longer exist only after heavy grid refinement. We describe a method for obtaining solutions for coplanar and near-coplanar cases that consist of only regular structures, independent of grid refinement. The method, referred to as Compound Wave Modification (CWM), involves removing the flux associated with non-regular structures and can be used for simulations in two- and three-dimensions because it does not require explicitly tracking an Alfvén wave. For a near-coplanar case, and for grids with 213 points or less, we find root-square-mean-errors (RMSEs) that are as much as 6 times smaller. For the coplanar case, in which non-regular structures will exist at all levels of grid refinement for standard FVMs, the RMSE is as much as 25 times smaller.

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