The goal of the present work is to solve the magnetohydrodynamic (MHD) system of extended generalized Lagrange multiplier (EGLM) formulation with Galilean invariance (G-EGLM MHD equations) through a modified path-conservative HLLEM finite-volume method. A second-order least-squares reconstruction with Venkatakrishnan limiter is employed for state variables, and a solenoidality-preserving condition is considered for the magnetic field with the purpose of magnetic divergence cleaning. The two-stage Runge–Kutta time-integration method is utilized to advance the MHD governing equations. Compared with the original path-conservative HLLEM method, the modified method in this paper is shock stable and is able to adjust the diffusion according to the smoothness of the physical flow so as to automatically apply more diffusion near strong shocks and less in smooth regions near rarefaction waves and at contact discontinuities. Meanwhile, it can be robustly defined in the low plasma-β region. After several tests of smooth Alfvn wave, strong Lax, odd–even perturbation, and blast-wave problems, the large-scale structures of the solar corona for Carrington Rotation 2185 are numerically modeled in a six-component grid system of spherical coordinates with input from a Carrington rotation synoptic map provided by the Helioseismic and Magnetic Imager. Numerical results show the model’s capability of producing a structured solar wind in agreement with the observations.

本工作的目的是通过改进的路径保守的HLLEM有限体积方法，解决具有伽利略不变性的广义广义拉格朗日乘数（EGLM）公式的磁流体动力学（MHD）系统。对于状态变量，使用带有Venkatakrishnan限制器的二阶最小二乘重建，并且为了进行磁发散清洗，考虑了磁场的螺线保持条件。两阶段Runge-Kutta时间积分方法用于推进MHD控制方程。与原始的保守路径HLLEM方法相比，本文中的改进方法是冲击稳定的，并且能够根据物理流动的平滑度来调整扩散，从而在强冲击附近自动施加更多的扩散，而在稀疏波附近以及接触不连续处的平滑区域自动施加更少的扩散。同时，可以在低等离子条件下稳健地定义β区。在对光滑的Alfvn波，强Lax，奇偶摄动和爆炸波问题进行了几次测试之后，对Carrington旋转2185的太阳日冕的大型结构进行了数值模拟，该模型由具有输入的球面坐标的六分量网格系统组成来自Helioseismic and Magnetic Imager提供的Carrington旋转天气地图。数值结果表明该模型产生与观测结果一致的结构化太阳风的能力。