Characteristic boundary conditions for magnetohydrodynamics: The Brio–Wu shock tube

Abstract

In the present paper we develop and test a characteristic-based boundary condition (BC) scheme for the compressible magnetohydrodynamic equations, as the extension of a characteristic gasdynamics BC model. We use a Harten–Yee finite volume scheme for the spatial discretization of the domain, and a TVD Backward Euler time integrator for the sake of robustness. First we verify that the scheme works correctly for gasdynamic initial conditions (i.e., when B=0), comparing with both analytical and experimental data. We then test the BC scheme with the Brio and Wu shock tube for two different types of boundaries: an open end and solid walls. We present a comparison between results obtained with the zeroth-order extrapolated BC scheme and the characteristic scheme developed. For a solid wall condition, we found discrepancies between both schemes when perturbations in the transverse magnetic field component (By) reach the boundaries. Also for the open end condition some discrepancies appear between the characteristic and extrapolated schemes, presenting the latter some instabilities. The results obtained with the characteristic scheme are smoother but presented a different wave pattern, which we believe is physical.