TVD Scheme for the Numerical Simulation of the Axisymmetrical Selfgravitating MHD Flows

The explicit quasi-monotonic conservative TVD scheme and numerical method for the solution of the gravitational MHD equations are developed. The 2D numerical code for the simulation of multidimensional selfgravitating MHD flows on the Eulerian cylindrical grid is constructed. The results of test calculations show that the code has a good mathematical and computational properties and can be applied to the solution of a wide class of plasma physics and astrophysics problems. We have simulated, for example, a collapse of magnetized rotating protostellar clouds.