Removal of pseudo-convergence in coplanar and near-coplanar Riemann problems of ideal magnetohydrodynamics solved using finite volume schemes
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 Alfvn 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.
pseudo-convergence coplanar finite volume ideal mhd