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.

Prediction of Solar Coronal Structures Using Fourier Neural Operators Based on the Solar Photospheric Magnetic Field Observation

“…Using these methods, numerous comprehensive physics-based numerical models have been developed to study the background solar wind. Examples include the Space Weather Modeling Frame (SWMF) (Gombosi et al, 2018;Tóth et al, 2005Tóth et al, , 2012, the Hybrid Heliospheric Modeling System (HHMS) (Detman et al, 2006(Detman et al, , 2012Smith et al, 2008;Wu et al, 2007), the Coronal and Heliospheric Model (CORHEL) (Linker et al, 1994(Linker et al, , 1999(Linker et al, , 2010Odstrcil, 2003;Riley et al, 2001), the Solar InterPlanetary-Conservative Element Solution Element (SIP-CESE) (Feng et al, 2007(Feng et al, , 2010(Feng et al, , 2012(Feng et al, , 2015Hu et al, 2008), the coronal model by an implicit high-order reconstructed discontinuous Galerkin (Liu et al, 2023), the 3D MHD model proposed by Hayashi and others (Hayashi, 2005(Hayashi, , 2013Hayashi et al, 2022) and many others. For an in-depth overview of existing 3D MHD models, see the first chapter of Feng (2020).…”