A new finite-difference method for simulation of compressible MHD flows applicable to a very large class of problems is presented. The method is based on using of magnetic quasi-gasdynamic equations (QMHD equations) which are actually Navier-Stokes equations supplemented by Faraday equations, to which an averaging procedure over a small time interval has been applied. QMHD equations are discretized on a computational grid by central differences. The averaging allows to stabilize a numerical solution without application of additional limiting functions. Non-divergence constraint on magnetic field is provided by application of the Stokes theorem. The numerical solution of 3D test problems are presented. Among them there is a blast wave propagation through magnetized medium, interaction of a shock wave with a cloud and Orszag-Tang vortex problem, extended for 3D case. Also the preliminary simulations of magnetically confined plasma pinch are presented.

magnetic quasi-gasdynamic, QMHD, MHD flows, finite difference algorithm, central difference approximations

Mathematical modelling in actual problems of science and technics