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[1] We present our newly developed numerical model of the solar wind interaction with the planet Venus. The model solves three-dimensional, 10-ion-species magnetohydrodynamic (MHD) equations using a total variation diminishing monotonic upstream scheme for conservation laws, which is implemented on an unstructured grid system. These equations describe the dynamics of both the solar wind and the planetary ionosphere. An excellent performance of the model is verified by comparing our numerical results with the existing numerical and observational data. In particular, profiles of the magnetic field, number densities, velocity, and transterminator flux of ionospheric plasma are shown to reproduce the observational findings. A main goal of this paper is to present the numerical model and its performance for the general dynamics and structures of the solar wind interaction with the ionosphere of Venus.

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Abstract. In this paper we review several mathematical aspects in numerical methods for magnetohydrodynamic equations. The intrinsic complexity and the requirements of the selenoidity condition make numerical solutions of these equations a formidable task. We present results of advanced numerical simulations for a complex system, which reveal that the numerical methods cope very well with this task.