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.

The main aim of the current work is to apply the Roe+Lax–Friedrichs (LF) hybrid entropy-stable scheme to the simulation of the three-dimensional ambient solar wind. The governing equations for the solar wind flow and magnetic field utilize the entropy-consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics (MHD) equations, which are symmetric and Galilean invariant with some nonconservative terms proportional to the divergence of magnetic field or the gradient of the Lagrange multiplier ψ. By using solenoidality-preserving and non-negativity-preserving reconstruction, the divergence error is further constrained, and the densities and pressures are reliably guaranteed. Moreover, the entropy is used as an auxiliary equation to completely avoid the appearance of negative pressure, which is independent of any numerical flux and can be retrofit into any MHD equations straightforwardly. All the properties referred to above make the newly developed scheme more handy and robust to cope with the high Mach number or low plasma β situations. After the experiments of the entropy consistency and the robustness of the proposed entropy-stable scheme through two simple tests, we carry out the simulation of the large-scale solar wind structures for Carrington Rotation 2183 (CR 2183) in a six-component grid system with the initial potential field obtained from the Helioseismic and Magnetic Imager magnetogram by retaining spherical harmonics of degree 50. The comparisons of the numerical results with the remote sensing observations and in situ data show that the new model has the capability to produce structured solar wind.

In this paper, we employ a path-conservative HLLEM finite-volume method (FVM) to solve the solar wind magnetohydrodynamics (MHD) systems of extended generalized Lagrange multiplier (EGLM) formulation with Galilean invariance (G-EGLM MHD equations). The governing equations of single-fluid solar wind plasma MHD are advanced by using a one-step MUSCL-type time integration with the logarithmic spacetime reconstruction. The code is programmed in FORTRAN language with Message Passing Interface parallelization in spherical coordinates with a six-component grid system. Then, the large-scale solar coronal structures during Carrington rotations (CRs) 2048, 2069, 2097, and 2121 are simulated by inputting the line-of-sight magnetic field provided by the Global Oscillation Network Group (GONG). These four CRs belong to the declining, minimum, rising, and maximum phases of solar activity. Numerical results basically generate the observed characteristics of structured solar wind and thus show the code’s capability of simulating solar corona with complex magnetic topology.