  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.
