We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and solution element(CESE) method in general curvilinear coordinates on a six-component grid system. As a preliminary study, this paper is to present the model's numerical results of the quasi-steady state and the dynamics of the Earth's magnetosphere under steady solar wind flow with due northward interplanetary magnetic field(IMF). The model results are found to be in good agreement with those published by other numerical magnetospheric models.
A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.
