High-Order Finite Difference Schemes Based on Symmetric Conservative Metric Method: Decomposition, Geometric Meaning and Connection with Finite Volume Schemes

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Xiaogang Deng

Huajun Zhu

Yaobing Min

Huayong Liu

Meiliang Mao

Guangxue Wang

  1. A viscous-term subcell limiting approach for high-order FR/CPR method in solving compressible Navier-Stokes equations on curvilinear grids

    Zhu, Huajun | Yan, Zhen-Guo | Liu, Huayong | Mao, Meiliang | Deng, Xiaogang

    Journal of Computational Physics, Vol. 514 (2024), Iss. P.113240

    https://doi.org/10.1016/j.jcp.2024.113240 [Citations: 1]
  2. WCNS schemes and some recent developments

    Chen, Yaming | Deng, Xiaogang

    Advances in Aerodynamics, Vol. 6 (2024), Iss. 1

    https://doi.org/10.1186/s42774-023-00165-x [Citations: 2]