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Volume 31, Issue 4
A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes

Guo-Quan Shi, Huajun Zhu & Zhen-Guo Yan

DOI: 10.4208/cicp.OA-2021-0165

Commun. Comput. Phys., 31 (2022), pp. 1215-1241.

Published online: 2022-03

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  • Abstract

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.

  • Keywords

Flux reconstruction/correction procedure via reconstruction, shock capturing, subcell limiting, unstructured meshes.

  • AMS Subject Headings

65D05, 65M06, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-1215, author = {Shi , Guo-QuanZhu , Huajun and Yan , Zhen-Guo}, title = {A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {4}, pages = {1215--1241}, abstract = {

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0165}, url = {http://global-sci.org/intro/article_detail/cicp/20382.html} }
TY - JOUR T1 - A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes AU - Shi , Guo-Quan AU - Zhu , Huajun AU - Yan , Zhen-Guo JO - Communications in Computational Physics VL - 4 SP - 1215 EP - 1241 PY - 2022 DA - 2022/03 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0165 UR - https://global-sci.org/intro/article_detail/cicp/20382.html KW - Flux reconstruction/correction procedure via reconstruction, shock capturing, subcell limiting, unstructured meshes. AB -

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.

Guo-Quan Shi, Huajun Zhu & Zhen-Guo Yan. (2022). A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes. Communications in Computational Physics. 31 (4). 1215-1241. doi:10.4208/cicp.OA-2021-0165
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