"Modeling of magnetorotational instability evolution using a parallel RKDG algorithm for the magnetohydrodynamic system of equations"
Galanin M.P., Lukin V.V., and Shapovalov K.L.

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.

Keywords: magnetorotational instability, magnetohydrodynamics, RKDG method, parallel programming, MPI.

  • Galanin M.P. – Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; ploshchad’ Miusskaya 4, Moscow, 125047, Russia; Professor, Head of Department, e-mail: galan@keldysh.ru
  • Lukin V.V. – Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; ploshchad’ Miusskaya 4, Moscow, 125047, Russia; Ph.D., Scientist, e-mail: vvlukin@gmail.com
  • Shapovalov K.L. – Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; ploshchad’ Miusskaya 4, Moscow, 125047, Russia; Senior Laboratory Assistant, e-mail: ShapovalovKL@yandex.ru