An improved CESE method and its application to steady-state coronal structure simulation

This paper presents an improved space-time conservation element and solution element (CESE) method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics (MHD) equations. The improved CESE method can improve the solution quality even with a large disparity in the Courant number (CFL) when using a fixed global marching time. Moreover, for a small CFL (say < 0.1), the method can significantly reduce the numerical dissipation and retain the solution quality, which are verified by two benchmark problems. And meanwhile, comparison with the original CESE scheme shows better resolution of the improved scheme results. Finally, we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.