Modified path-conservative HLLEM scheme for magnetohydrodynamic solar wind simulations

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 Alfvén 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.