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Volume 23, Issue 5
High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws

Huajun Zhu, Zhenguo Yan, Huayong Liu, Meiliang Mao & Xiaogang Deng

DOI: 10.4208/cicp.OA-2017-0032

Commun. Comput. Phys., 23 (2018), pp. 1355-1392.

Published online: 2018-04

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  • Abstract

A type of hybrid WCNS and CPR method for solving conservation laws on hybrid structured and unstructured meshes is proposed. WCNS on structured grid is conjoined with CPR on unstructured grid through CPR on structured grid. The main hybrid technique becomes coupling WCNS and CPR on curvilinear structured grid. Calculation of grid metrics, interpolation methods of physical coordinates and state variables, and computation of Riemann flux near coupling interface are designed to maintain the expected high order accuracy and to satisfy discrete geometric conservation laws in the whole computational domain. Third-order schemes and fifth-order schemes are considered. Numerical simulations show that the proposed hybrid WCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation law and have good balance of computational efficiency and grid flexibility.

  • Keywords

Weighted compact nonlinear scheme (WCNS), Correction procedure via reconstruction (CPR), hybrid schemes, hybrid grid, high-order accuracy.

  • AMS Subject Headings

65D05, 65M06, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-23-1355, author = {Huajun Zhu, Zhenguo Yan, Huayong Liu, Meiliang Mao and Xiaogang Deng}, title = {High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {5}, pages = {1355--1392}, abstract = {

A type of hybrid WCNS and CPR method for solving conservation laws on hybrid structured and unstructured meshes is proposed. WCNS on structured grid is conjoined with CPR on unstructured grid through CPR on structured grid. The main hybrid technique becomes coupling WCNS and CPR on curvilinear structured grid. Calculation of grid metrics, interpolation methods of physical coordinates and state variables, and computation of Riemann flux near coupling interface are designed to maintain the expected high order accuracy and to satisfy discrete geometric conservation laws in the whole computational domain. Third-order schemes and fifth-order schemes are considered. Numerical simulations show that the proposed hybrid WCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation law and have good balance of computational efficiency and grid flexibility.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0032}, url = {http://global-sci.org/intro/article_detail/cicp/11219.html} }
TY - JOUR T1 - High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws AU - Huajun Zhu, Zhenguo Yan, Huayong Liu, Meiliang Mao & Xiaogang Deng JO - Communications in Computational Physics VL - 5 SP - 1355 EP - 1392 PY - 2018 DA - 2018/04 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0032 UR - https://global-sci.org/intro/article_detail/cicp/11219.html KW - Weighted compact nonlinear scheme (WCNS), Correction procedure via reconstruction (CPR), hybrid schemes, hybrid grid, high-order accuracy. AB -

A type of hybrid WCNS and CPR method for solving conservation laws on hybrid structured and unstructured meshes is proposed. WCNS on structured grid is conjoined with CPR on unstructured grid through CPR on structured grid. The main hybrid technique becomes coupling WCNS and CPR on curvilinear structured grid. Calculation of grid metrics, interpolation methods of physical coordinates and state variables, and computation of Riemann flux near coupling interface are designed to maintain the expected high order accuracy and to satisfy discrete geometric conservation laws in the whole computational domain. Third-order schemes and fifth-order schemes are considered. Numerical simulations show that the proposed hybrid WCNS-CPR schemes can obtain designed accuracy, satisfy geometric conservation law and have good balance of computational efficiency and grid flexibility.

Huajun Zhu, Zhenguo Yan, Huayong Liu, Meiliang Mao and Xiaogang Deng. (2018). High-Order Hybrid WCNS-CPR Schemes on Hybrid Meshes with Curved Edges for Conservation Laws I: Spatial Accuracy and Geometric Conservation Laws. Communications in Computational Physics. 23 (5). 1355-1392. doi:10.4208/cicp.OA-2017-0032
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