A family of approximate solutions to the MHD Riemann problem retaining the shock relations (Q1974756)

Efficient numerical methods based on exact or approximate local solution of the one-dimensional Riemann problem are widely employed in calculations of multidimensional gas flows. These methods are difficult to exend to the equations of ideal magnetohydrodynamics (MHD) because the corresponding exact solution is multiform. The authors construct a family of approximate solutions to the one-dimensional Riemann problem posed for the MHD equations. These solutions are characterized by exact fulfilment of the shock relations.