Modeling the Solar Corona with an Implicit High-order Reconstructed Discontinuous Galerkin Scheme

Abstract

The present study aims to apply an implicit high-order reconstructed discontinuous Galerkin (DG) scheme (rDG(P 1 P 2)) to simulate the steady-state solar corona. In this scheme, a piecewise quadratic polynomial solution, P 2, is obtained from the underlying piecewise linear DG solution, P 1, by least-squares reconstruction with a weighted essentially nonoscillatory limiter. The reconstructed quadratic polynomial solution is then used for the computation of the fluxes and source terms. In addition, an implicit time integration method with large time steps is considered in this work. The resulting large linear algebraic system of equations from the implicit discretization is solved by the cellwise relaxation implicit scheme which can make full use of the compactness of the DG scheme. The code of the implicit high-order rDG scheme is developed in Fortran language with message passing interface parallelization in Cartesian coordinates. To validate this code, we first test a problem with an exact solution, which confirms the expected third-order accuracy. Then we simulate the solar corona for Carrington rotations 2167, 2183, and 2210, and compare the modeled results with observations. We find that the numerical results basically reproduce the large-scale observed structures of the solar corona, such as coronal holes, helmet streamers, pseudostreamers, and high- and low-speed streams, which demonstrates the capability of the developed scheme.