Simulation of three-dimensional nonideal MHD flow at high magnetic Reynolds number

A conservative TVD scheme is adopted to solve the equations governing the three-dimensional flow of a nonideal compressible conducting fluid in a magnetic field. The eight-wave equations for magnetohydrodynamics (MHD) are proved to be a non-strict hyperbolic system, therefore it is difficult to develop its eigenstructure. Powell developed a new set of equations which cannot be numerically simulated by conservative TVD scheme directly due to its non-conservative form. A conservative TVD scheme augmented with a new set of eigenvectors is proposed in the paper. To validate this scheme, 1-D MHD shock tube, unsteady MHD Rayleigh problem and steady MHD Hartmann problem for different flow conditions are simulated. The simulated results are in good agreement with the existing analytical results. So this scheme can be used to effectively simulate high-conductivity fluids such as cosmic MHD problem and hypersonic MHD flow over a blunt body, etc.