Implicit dual-time stepping method for a solar wind model in spherical coordinates

In this paper, an implicit dual-time stepping scheme based on the finite volume method in spherical coordinates with a six-component grid system is developed to model the steady state solar wind. By adding a pseudo-time derivative to the magnetohydrodynamics equations for the solar wind plasma, the governing equations are solved implicitly at each physical time step by advancing in pseudo time. As a validation, ambient solar wind for Carrington rotation 2048 has been studied. Numerical tests with different Courant factors show its capability of producing structured solar wind and that the physical time step can be enlarged to be one hundred times that of the original one. Our numerical results have demonstrated overall good agreements with the observations.