Divergence-free finite-difference method for 2D ideal MHD

The divergence-free finite-difference scheme for 2d ideal MHD using triangular unstructured staggered grids is described. In this approach the density, pressure and velocity fields are attributed to grid cells and magnetic field is defined by its normal components in cells edges. The HLLD approximate Riemann solver is used to compute the numerical flux of gas-dynamics variables at edges. It also provides the electrical field values used to compute the magnetic field. The magnetic field is interpolated into the cells using Raviart — Thomas basis functions. The algorythm is implemented in parallel numerical code. The method is tested on several well-known two-dimensional MHD problems. (paper)