In the past three decades, solar-terrestrial physicists have introduced many kinds of numerical schemes in computational fluid mechanics to magnetohydrody-namic system in order to simulate various phenomena of solar-terrestrial physics. Along with the recent advance of space weather, great attention has been paid to the development of quick convergence and high resolution numerical schemes of MHD system for the purpose of solar wind storm simulation or establishing numerical prediction methods of space weather. The numerical study of solar wind has undergone a transit from its early simulation problems in supersonic and superAlfvenic domain to the recent works from solar surface, interplanetary space to the interaction between solar wind and the earth's magnetosphere. In this paper, according to the characteristics of numerically modeling solar wind, a new numerical scheme of TVD type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account of the quality such as convergence, stability, resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method. Under typical physical parameters on the solar surface, using a dipole as initiation, the steady state numerical results for the solar wind flow is reached by time-relaxation approach. This shows that this numerical model has potential application in modeling solar wind of complex magnetic field and realistic solar-interplanetary storms.
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