Numerical solutions of one-dimensional MHD equations by a fluctuation approach

Abstract

In this paper a higher-order Godunov method for one-dimensional solutions of the ideal MHD (magnetohydrodynamics) equations is presented. The method uses a fluctuation approach and includes a new sonic fix and a new Roe averaging. After a short introduction the MHD equations in conservative form are given. The flux is rearranged such that the eigenstructure is not changed. This rearrangement allows full Roe averaging for any value of adiabatic index (contrary to Brio and Wu's conclusion). A new procedure to get Roe-averaged MHD fields at the interfaces between left and right states is then presented and some useful identities are given. Next the second-order-limited fluctuation approach is presented in full detail. The new sonic fix for MHD and the procedure for applying this fix to the sonic points are then given in detail. Numerical results obtained with the described method are presented. Finally, conclusions are given.