Lukin

The Runge–Kutta discontinuous Galerkin method for an ideal MHD system of equations on the unstructured mesh for axisymmetric cases was considered. An algorithm of divergence-free magnetic field reconstruction in cylindrical coordinates was given. This algorithm allows one to obtain physically appropriate computation results with a high order of accuracy. A mathematical simulation of magneto-rotational instability in the shell of an accreting protostar was carried out. The obtained results were illustrated and discussed. These results showed that the magneto-rotational instability leads to formation of large-scale structures and causes transfer of angular momentum to the circumference of a plasma cloud.