摘要
In this paper,a new numerical scheme of Total Variation Diminishing (TVD) Mac-Cormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking intoaccount of the characteristics such as convergence,stability, resolution.This new schemeis established by solving the MHD equations with a TVD modified MacCormack schemefor 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 MHDproblems,a self-similar Cauchy problem with the discontinuous initial data consisting ofconstant states, and the collision of two fast MHD shocks, and two-dimensional Orszagand Tang's MHD vortex problem are discussed with the numerical results conformingto the existing results obtained by the Roe type TVD,the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme.The numerical tests showthat this two-step TVD MacCormack numerical scheme for MHD system is of robustoperation in the presence of very strong waves, thin shock fronts,thin contact and slipsurface discontinuities.