Implicit kinetic schemes for the euler and the ideal magnetohydrodynamics equations

Abstract

The implicit kinetic schemes, namely the Kinetic Flux-Vector Split (KFVS) and the Kinetic Wave/Particle Split (KWPS) schemes are derived for the Euler and the ideal MHD equations. The schemes are applied to compute the flow in a 1-D shock tube and the 2-D flowfield due to a cylindrical explosion with and without the magnetic field. For the ideal 2-D MHD equations, the homogeneity of the flux vector is achieved by employing the approach due to MacCormack, and a Poisson solver is used at every time- step to enforce the solenoidal condition on the magnetic field. To the authors' knowledge, this is the first time that the implicit kinetic schemes have been formulated for the Euler and the ideal MHD equations. © 2002 by the authors.