中文摘要：

开发高性能的磁流体力学数值模拟方法是提高空间天气数值预报研究的一个重要方面.有限体积法的逆风分裂格式具有良好的间断捕获能力,Steger-Warming和AUSM（Advection Upstream Splitting Method）是逆风分裂格式FVS（Flux Vector Splitting）方法中具有代表性的两种格式.采用这两种格式求解具有伽利略不变性的扩展型广义拉格朗日乘子磁流体力学（EGLM-MHD）方程组,对Orszag-Tang涡流问题和三维爆炸波问题进行数值模拟,结果表明两种格式均能得到稳定精确的数值结果.与StegerWarming格式相比,AUSM格式产生的磁场散度误差更小,计算速度更快.

英文摘要：

To develop a high performance MHD numerical simulation method is an important factor in research of numerical prediction of space weather. The upwind flux splitting scheme based on finite volume method has good ability to capture discontinuities. Steger-Warming and AUSM （Advection Upstream Splitting Method） schemes are two outstanding upwind flux splitting scheme, which are classified as FVS （Flux Vector Splitting） method. In this paper, these two schemes are applied to solve the Extended Generalized Lagrange Multiplier Magnetohydrodynamics （EGLM-MHD） equation with Galilean invariance. Results obtained from Orszag-Tang vortex and three-dimensional blastwave problem indicate that those two schemes are both robust and accurate. Particularly, AUSM schemeis superior to Steger-Warming scheme in divergence error control and computational speed