Modified Path-conservative HLLEM Scheme for Magnetohydrodynamic Solar Wind Simulations

Abstract

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.

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

“…= (e.g., Ogino & Walker 1984;Tanaka 1994Tanaka , 1995Powell et al 1999;Feng et al 2010;Fuchs et al 2010Fuchs et al , 2011aGuo 2015;Guo et al 2016;Li et al , 2021aWang et al 2018). The governing MHD equations read,…”

“…In Figure 12, we compare the radial speeds and the radial magnetic field polarities at 20R s obtained from the simulated results with those mapped from the in situ measurements near the Earth available in the OMNI archive (King & Papitashvili 2005) by using a ballistic approximation (Yang et al 2012;Feng et al 2017;Li et al , 2021a for both CRs 2177 and 2212. For CR 2177, the modeled results roughly capture four leading speed peaks centered around the longitudes of 25°, 160°, 250°, and 310°, respectively.…”