EXTENSION OF THE PIECEWISE PARABOLIC METHOD TO MULTIDIMENSIONAL IDEAL MAGNETOHYDRODYNAMICS

An extension of the piecewise parabolic method to treat multi-dimensional ideal magnetohydrodynamical equations is presented in this paper. The multidimensional scheme is constructed from a one-dimensional functioning code based on the dimensional splitting method originally suggested by Strang. The functioning code is built upon a nonlinear Riemann solver for ideal MHD equations recently developed by the authors. The correctness of the scheme is tested in the steepening of waves in both one- and two-dimensional situations and in Various MHD shock-tube problems which involve all the discontinuities in ideal MHD. The robust character of the scheme is demonstrated in the shock-tube problems and in the interaction between MHD shocks and a cloud. The results of these problems show that the scheme keeps the principal advantages of a high-order Godunov scheme: robust operation in the presence of very strong waves, thin shock fronts with little attendant noise generation, and thin contact discontinuity, (C) 1994 Academic Press. Inc.