Brio and Wu Shock Tube
Brio, M. & C.C. Wu, "An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics", Journal of Computational Physics, 75, 400-422 (1988). The test is described in Section V.
This test is an MHD shocktube, where the right and left states are initalized to different values. The left state is initialized as (ρ, vx, vy, vz, By, Bz, p) = [1,0,0,1,0,1] and the right state [0.125,0,0,-1,0,0.1]. Bx=0.75 and γ = 2. The hydrodynamic portion of the initial conditions are the same as for the Sod shock tube problem.
This example tests whether the code can accurately represent the shocks, rarefactions, contact discontinuities, and the compound structures of MHD. The test is now a standard for MHD codes.
Results computed with Athena using the second order Roe solver with 400 grid points (squares) and 10,000 grid points (solid line). The plot shows from left to right: a fast rarefaction, a slow compound wave, a contact discontinuity, a slow shock, and a fast rarefaction wave. These results can be compared to Fig. 2 in the reference.
Page by Ian Parrish, February 2004.