A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations (Communications in Computational Physics, 2023)
In this paper, we construct a two-dimensional third-order space-time conservation element and solution element (CESE) method and apply it to the magnetohydrodynamics (MHD) equations. This third-order CESE method preserves all thefavorable attributes of the original second-order CESE method, such as: (i) flux conservation in space and time without using an approximated Riemann solver, (ii) genuinemulti-dimensional algorithm without dimensional splitting, (iii) the use of the mostcompact mesh stencil, involving only the immediate neighboring cells surroundingthe cell where the solution at a new time step is sought, and (iv) an explicit, unifiedspace-time integration procedure without using a quadrature integration procedure.In order to verify the accuracy and efficiency of the scheme, several 2D MHD testproblems are presented. The result of MHD smooth wave problem shows third-orderconvergence of the scheme. The results of the other MHD test problems show that themethod can enhance the solution quality by comparing with the original second-orderCESE scheme.