A High-Order Godunov-Type Scheme for Shock Interactions in Ideal Magnetohydrodynamics

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Abstract
A high-order Godunov-type scheme is developed for the shock interactions in ideal magnetohydrodynamics (MHD). The scheme is based on a nonlinear Riemann solver and follows the basic procedure in the piecewise parabolic method. The scheme takes into account all the discontinuities in ideal MHD and is in a strict conservation form. The scheme is applied to numerical examples, which include shock-tube problems in ideal MHD and various interactions between strong MHD shocks. All the waves involved in the corresponding Riemann problems are resolved and are correctly displayed in the simulation results. The correctness of the scheme is shown by the comparison between the simulation results and the solutions of the Riemann problems. The robustness of the scheme is demonstrated through the numerical examples. It is shown that the scheme offers the principle advantages of a high-order Godunov-type scheme: robust operation in the presence of very strong waves, thin shock fronts, and thin contact and slip surface discontinuities.