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Volume 34, Issue 1
A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations

Yufen Zhou & Xueshang Feng

Commun. Comput. Phys., 34 (2023), pp. 94-115.

Published online: 2023-08

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  • Abstract

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.

  • AMS Subject Headings

65M08, 76W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-94, author = {Zhou , Yufen and Feng , Xueshang}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0265}, url = {http://global-sci.org/intro/article_detail/cicp/21881.html} }
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 -

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.

Zhou , Yufen and Feng , Xueshang. (2023). A Two-Dimensional Third-Order CESE Scheme for Ideal MHD Equations. Communications in Computational Physics. 34 (1). 94-115. doi:10.4208/cicp.OA-2022-0265
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