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This paper is concerned with a numerical solutions of two-component magnetohydrodynamic equations. While a hyperbolic system of wave equations admits a shock solution as a result of the selenoidality condition the MHD equations are not strictly hyperbolic. As a consequence of that these equations require special numerical treatment. An application of a resulting numerical code to a problem of solar wind interaction with the ionosphere of the planet Venus is presented.

Godunov-type methods for two-component magnetohydrodynamic equations