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

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.