A CLASS OF TWO-STEP TVD MACCORMACK TYPE NUMERICAL SCHEME FOR MHD EQUATIONS

In this paper, a new numerical scheme of Total Variation Diminishing （TVD） Mac-Cormack type for MagnetoHydroDynamic （MHD） equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang’s MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme, and Weighted Essentially Non-Oscillatory （WENO） scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation