High-Order Finite Difference Schemes Based on Symmetric Conservative Metric Method: Decomposition, Geometric Meaning and Connection with Finite Volume Schemes
Year: 2020
Author: Xiaogang Deng, Huajun Zhu, Yaobing Min, Huayong Liu, Meiliang Mao, Guangxue Wang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 436–479
Abstract
High-order finite difference schemes (FDSs) based on symmetric conservative metric method (SCMM) are investigated. Firstly, the decomposition and geometric meaning of the discrete metrics and Jacobian based on SCMM are proposed. Then, high-order central FDS based on SCMM is proved to be a weighted summation of second-order finite difference schemes (FDSs). Each second-order FDS has the same vectorized surfaces and cell volume as a second-order finite volume scheme (FVS), and the cell volume is uniquely determined by the vectorized surfaces. Moreover, the decomposition and connection with FVSs are also discussed for general high-order FDSs. SCMM can be applied for high-order weighted compact nonlinear scheme (WCNS). Numerical experiments show superiority of high-order WCNS based on SCMM in stability, accuracy and ability to compute flows around complex geometries. The results in this paper may to some extent explain why high-order FDSs based on SCMM can solve problems with complex geometries and may give some guidance in constructing high-order FDSs on curvilinear coordinates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2017-0243
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 436–479
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 44
Keywords: High-order finite difference schemes symmetric conservative metric method finite volume schemes complex geometries.
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