Direct discontinuous Galerkin method for potential magnetic field solutions

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 solved by means of the time-dependent method, i.e., introducing a pseudo-time term into the Laplace’s equation and changing the boundary value problem into the initial-boundary value problem. The steady-state solution of the initial-boundary value problem is the solution of the Laplace’s equation to be solved. This formulation facilitates the implementation of the DDG discretization. In order to validate the DDG-PFSS solver, we test a problem with the exact solution, which demonstrates the effectiveness and third-order accuracy of the solver. Then we apply it to the extrapolation for the coronal potential magnetic field. We use the integral GONG synoptic magnetogram of Carrington rotation (CR) 2060 as the boundary condition and achieve the global potential magnetic field solution by the DDG-PFSS solver. 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 seen as a contribution to the numerical methods for obtaining the global potential magnetic field solutions of the solar corona.