Modeling of magnetorotational instability evolution using a parallel RKDG algorithm for the magnetohydrodynamic system of equations

A parallel algorithm of the RKDG (Runge-Kutta Discontinuous Galerkin) method for axisymmetric 2D ideal MHD equations on unstructured triangular grids is developed. An algorithm of divergence-free magnetic field reconstruction in the cylindrical coordinate system is proposed to obtain physically adequate numerical results with a high degree of accuracy. A high level of the developed parallel code scalability is shown for multiprocessor systems. The parallelization efficiency is analyzed using the K-100 cluster installed at the Keldysh Institute of Applied Mathematics. The results of modeling the magnetorotational instability in a accreting protostar shell are discussed.