A 2D Fourth-Order CESE Scheme for Solving the Ideal MHD Equations (Communications in Computational Physics, 2025)
We construct a two-dimensional fourth-order space-time conservation element and solution element (CESE) schemes for solving the ideal magnetohydrodynamics (MHD) equations. In the CESE scheme, the flow variables are calculated byusing the same procedure as that of the original second-order CESE scheme. Thescheme preserves most favorable attributes of the original second-order CESE method.Moreover, it is simple and easy to program. The numerical example for the smoothAlfvén wave problem suggests that the scheme can achieve the fourth-order accuracyfor smooth solutions. In order to verify the efficiency of the schemes, we simulate several 2D MHD problems. We find that the fourth-order scheme can capture shocks anddetails of complex flow structures very well, and control the magnetic divergence efficiently. Moreover, the scheme is essentially CFL number insensitive schemes. The lastseveral complex test problems further verify the performance of proposed scheme.
Keywords: CESE method; fourth-order accuracy; MHD.