Supercomputer modelling of magnetohydrodynamical flows in cosmic plasma

The paper describes a new numerical method for solving the equations of ideal magnetohydrodynamics (MHD) based on the Godunov method, a combination of the Roe and Rusanov schemes, and a piecewise parabolic representation of the solution. The hybrid scheme for solving the Riemann problem is associated with the possibility to reproduce the numerical solution without singularities along the directions, which is especially important when the velocity and magnetic field components are reconstructed in the transverse direction. The numerical method is implemented as a software package for massively parallel supercomputers. On the NKS-1P cluster of the SSCC, studies of parallel implementation and computational experiments were carried out. A problem with an analytical solution was used as a test for the method verification. A numerical solution of the problem of the interaction of a of molecular hydrogen cloud with the incoming interstellar medium is considered.