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

CIMINO, A; KRAUSE, G.; ELASKAR, S.; COSTA, A.

COMPUTERS & FLUIDS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2016 vol. 127 p. 194 - 210

0045-7930

In the present paper we develop and test a characteristic-based boundary condition (BC) scheme forthe compressible magnetohydrodynamic equations, as the extension of a characteristic gasdynamics BCmodel. We use a Harten?Yee finite volume scheme for the spatial discretization of the domain, and aTVD Backward Euler time integrator for the sake of robustness. First we verify that the scheme workscorrectly for gasdynamic initial conditions (i.e., when B = 0), comparing with both analytical and exper-imental data. We then test the BC scheme with the Brio and Wu shock tube for two different types ofboundaries: an open end and solid walls. We present a comparison between results obtained with thezeroth-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 com-ponent (B y ) reach the boundaries. Also for the open end condition some discrepancies appear betweenthe characteristic and extrapolated schemes, presenting the latter some instabilities. The results obtainedwith the characteristic scheme are smoother but presented a different wave pattern, which we believe is physical