Difference Scheme with a Symmetry Analyzer for Equations of Magnetohydrodynamics

摘要

The paper proposes a computational algorithm for the numerical simulation of two-dimensional magnetohydrodynamic (MHD) flows, using a symmetry analyzer as an element of the numerical method. The algorithm is based on a finite-volume Godunov-type scheme with an approximate solution of the Riemann problem for calculating flows. A polar mesh is used, but the momentum and magnetic induction equations are approximated in a Cartesian coordinate system. It is assumed that the flows are either predominantly homogeneous plane-symmetric, or predominantly axisymmetric with respect to the grid’s axis. To reconstruct vector variables in the computational cells, a symmetry analyzer is used, which makes it possible to locally classify the flow as one of the indicated types. Depending on the type of the vector field, the corresponding components are used for its reconstruction.