Direct discontinuous Galerkin method for potential magnetic field solutions - Liu, XiaoJing; Feng, Xueshang; Lv, Jiakun; Wang, Xinyi; Zhang, Man (Frontiers in Astronomy and Space Sciences, 2022)
In this paper, we employ the direct discontinuous Galerkin (DDG) method for the first time to extrapolate the coronal potential magnetic field (PF) with the source surface (SS) and call the developed numerical model as the DDG-PFSS solver. In this solver, the Laplace's equation is transformed to be a diffusion equation via the pseudo-time technique. This formulation facilitates the implementation of the DDG discretization, and the steady-state solution of the diffusion equation recovers the same solution of the original Laplace's equation. We use the integral GONG synoptic magnetograms of Carrington rotation (CR) 2060 as boundary condition, and then the global potential magnetic field solution is achieved by the DDG-PFSS solver with pseudo-time relaxation method. The numerical results such as the coronal holes and streamer belts derived from the DDG-PFSS solver are in good agreement with those obtained from the spherical harmonic expansion method. Also, based on the numerical magnetic field and Wang-Sheeley-Arge model, the obtained solar wind speed is found to basically capture the structures of the high- and low-speed streams observed at 1 AU. These results suggest that the DDG-PFSS solver can be used as an interesting alternative to the existing methods for obtaining the global potential magnetic field solutions of the solar corona.