MHD Shock Refraction at an Inclined Density Interface

Shock wave refraction at a sharp density interface is a classical problem in hydrodynamics. Presently, we investigate the refraction of magnetohydrodynamic (MHD) shock waves at an inclined density interface. For a chosen incident shock strength, and Atwood ratio, the MHD shock refraction transitions from regular (all nonlinear waves meeting at a single point) into irregular when the inclined density interface angle is less than a critical value. The MHD shock refraction process results in a pair of outer fast shocks (reflected and transmitted) and a set of inner nonlinear magneto-sonic waves. By varying magnetic field strength, the latter waves can be slow shocks, slow expansion fans, intermediate shocks or slow-mode compound waves. A Mach stem occurs in an irregular MHD shock refraction, resulting in a quadruple-point in which the Mach stem, shocked contact and a pair of transmitted waves meet, and a triple-point in which the incident shock, fast reflected shock and the Mach stem meet. Since the MHD shock refraction is self-similar, we further explore by converting the initial value problem (IVP) into a boundary value problem (BVP) by a self-similar coordinate transformation. The self-similar solution to the BVP is numerically solved using an iterative method, and implemented using the p4est adaptive mesh framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in this method.