A New Numerical Implementation for Solar Coronal Modeling by an HLL Generalized Riemann Problem Solver

In this paper, we employ a Harten–Lax–van Leer (HLL) generalized Riemann problem (HLL-GRP) solver within the framework of a finite volume method to model 3D solar coronal structures for the first time. Based on the rotational invariance of magnetohydrodynamics (MHD) equations, the HLL-GRP solver is successfully implemented into 3D MHD simulations. To constrain the divergence of the magnetic field, the locally divergence-free weighted-least-squares-based essentially nonoscillatory reconstruction and the properly discretized Godunov–Powell source term are applied. To keep density and pressure positive, a positivity-preserving limiter is added to the reconstructed polynomials of density and pressure. We first test a 3D blast wave problem to preliminarily validate the effectiveness of the proposed scheme on Cartesian structured grid. Then, we further run our code on a six-component grid to numerically study the steady-state coronal structures of Carrington rotation 2218 during the solar minimum phase. A comparison with the two-stage Runge–Kutta scheme is performed for both the 3D blast wave problem and solar coronal problem. Numerical results of large-scale solar coronal structures are basically consistent with the observational characteristics, indicating the robustness of the proposed model.