A quasi-gas dynamic algorithm for the numerical solution of shallow water equations for magnetic hydrodynamics

In this paper the technique of the solution of the ideal magnetohydrodynamic equations in shallow water approximation for a one-dimensional case by means of quasi-gas dynamic algorithm is presented. Algorithm for an example two problems one-dimensional magnetohydrodynamic was tested. Algorithm is employed for two test-cases. For both tests the numerical solution converges to self-similar ones by mesh refinement.