Dual-Time Stepping Method for Solar Wind Model in Spherical Coordinates

Abstract:

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 ambient. The base numerical scheme is established by splitting the magnetohydrodynamics equations into a fluid part and a magnetic part, and a finite volume method is used for the fluid part and the constrained-transport method that can maintain the divergence-free constraint on the magnetic field is used for the magnetic induction part. By adding a pseudo-time derivative to the magnetohydrodynamics equations for solar wind plasma, the governing equations are solved implicitly at each physical time step by advancing in pseudo time. As validation, solar wind ambient for Carrington rotations for CR 1915 (solar minimum), CR 1930 (rising phase), CR 1965 (solar maximum) and CR 2030 (declining phase) have 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. Of importance, our numerical results have demonstrated overall good agreements with observations.