@Article{CiCP-34-1,
author = {Zhou, Yufen and Xueshang, Feng},
title = {A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations},
journal = {Communications in Computational Physics},
year = {2023},
volume = {34},
number = {1},
pages = {94--115},
abstract = {<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>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0265},
url = {https://global-sci.com/article/79361/a-two-dimensional-third-order-cese-scheme-for-ideal-mhd-equations}
}