TY - JOUR
T1 - A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations
AU - Zhou , Yufen
AU - Feng , Xueshang
JO - Communications in Computational Physics
VL - 1
SP - 94
EP - 115
PY - 2023
DA - 2023/08
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2022-0265
UR - https://global-sci.org/intro/article_detail/cicp/21881.html
KW - CESE method, third-order, MHD equations.
AB - <p style="text-align: justify;">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 the
favorable attributes of the original second-order CESE method, such as: (i) flux conservation in space and time without using an approximated Riemann solver, (ii) genuine
multi-dimensional algorithm without dimensional splitting, (iii) the use of the most
compact mesh stencil, involving only the immediate neighboring cells surrounding
the cell where the solution at a new time step is sought, and (iv) an explicit, unified
space-time integration procedure without using a quadrature integration procedure.
In order to verify the accuracy and efficiency of the scheme, several 2D MHD test
problems are presented. The result of MHD smooth wave problem shows third-order
convergence of the scheme. The results of the other MHD test problems show that the
method can enhance the solution quality by comparing with the original second-order
CESE scheme.</p>