Providing the divergence-free property of the magnetic field when solving the MHD equations by the RKDG method

A review of methods providing the divergence-free property of the magnetic field when solving the two-dimensional problems of magnetic hydrodynamics on triangular grids by the secondorder discontinuous Galerkin method is presented. Procedures for redistributing the numerical flows corresponding to the magnetic field in the full two-dimensional formulation in the Cartesian coordinates and in the two-dimensional axisymmetric case in the cylindrical coordinates, making it possible to suppress the growth of the numerical divergence of the magnetic field, are described. Test problems of the Orszag–Tang vortex and spherical explosion are considered.