Linear Discontinuity Sharpening for Highly Resolved and Robust Magnetohydrodynamics Simulations

ABSTRACT This study applies a reconstruction scheme, “hybrid MUSCL–THINC” for finite volume methods developed by Chiu et al., to magnetohydrodynamics (MHD) simulations. The scheme is a hybrid of monotone upstream‐centered schemes for conservation law (MUSCL) and a tangent of hyperbola interface capturing (THINC) scheme. THINC sharply captures discontinuous distributions of physical quantities by using a hyperbolic tangent function. Our investigation reveals that hybrid MUSCL–THINC is more oscillatory in MHD simulations than in gas dynamics simulations, owing to the greater number of physical variables and associated complex waves in MHD. Analytical results demonstrate that artificial compression by THINC is excessive for MHD shock waves, whereas it is effective for linear discontinuities, such as contact discontinuities. Therefore, we propose a modification in which the artificial compression by THINC is weakened in the vicinity of nonlinear discontinuities and applied only to linear regions. The new scheme is tested using one‐ and two‐dimensional MHD problems, and the results demonstrate that the scheme sharply captures linear discontinuities while avoiding numerical oscillations due to excessive artificial compression.