Modeling solar corona with implicit high-order reconstructed discontinuous Galerkin scheme

The present study aims to apply an implicit high-order reconstructed discontinuous Galerkin scheme (rDG(P1P2)) to simulate the steady-state solar corona. In this scheme, a piecewise quadratic polynomial solution, P2, is obtained from the underlying piecewise linear DG solution, P1, by the least-squares reconstruction with weighted essentially non-oscillatory (WENO) limiter. The reconstructed quadratic polynomial solution is then used for the computation of the fluxes and source terms. In addition, 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 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 exact solution, which confirms the expected third-order accuracy. Then we simulate the solar corona, and compare the modeled results with the observations. We find that there is an overall agreement between the simulated results and the observations, which demonstrates the capability of the developed scheme.