A third-order solar coronal model based on the finite volume method

A third-order solar coronal model based on the finite-volume method in Cartesian coordinates is developed in this paper. The high-order spatial accuracy of this model is obtained by the $K$-exact least-square reconstruction ($K$=2) in combination with a weighted biased average procedure (WBAP) limiter, while temporal discretization is performed using a third-order strong-stability preserving (SSP) {Runge-Kutta} method. To enforce the divergence-free constraint on the magnetic field, the generalized Lagrange multiplier formulation of the magnetohydrodynamic equations with Galilean invariance (GLM-MHD-GI) is adopted. Using the proposed model, we first examine two two-dimensional (2D) benchmark problems---the smooth sine wave problem and the Orszag-Tang vortex problem---to validate its third-order accuracy and shock-capturing capability. Subsequently, the model is applied to simulate the steady-state solar corona during Carrington rotation (CR) 2063. The results demonstrate that the model successfully reproduces large-scale coronal structures and that the third-order scheme yields a thinner current sheet than the second-order model.