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Effect of Nonuniform Grids on High-Order Finite Difference Method

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  18 January 2017

Dan Xu ,
Xiaogang Deng ,
Yaming Chen ,
Guangxue Wang  and
Yidao Dong
Dan Xu*
Affiliation:
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
Xiaogang Deng
Affiliation:
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
Yaming Chen
Affiliation:
College of Science, National University of Defense Technology, Changsha, Hunan 410073, China
Guangxue Wang
Affiliation:
School of Physics, Sun Yat-sen University, Guangzhou, Guangdong 510006, China
Yidao Dong
Affiliation:
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
*
*Corresponding author. Email:xudan5293417@yahoo.com (D. Xu)
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Abstract

The finite difference (FD) method is popular in the computational fluid dynamics and widely used in various flow simulations. Most of the FD schemes are developed on the uniform Cartesian grids; however, the use of nonuniform or curvilinear grids is inevitable for adapting to the complex configurations and the coordinate transformation is usually adopted. Therefore the question that whether the characteristics of the numerical schemes evaluated on the uniform grids can be preserved on the nonuniform grids arises, which is seldom discussed. Based on the one-dimensional wave equation, this paper systematically studies the characteristics of the high-order FD schemes on nonuniform grids, including the order of accuracy, resolution characteristics and the numerical stability. Especially, the Fourier analysis involving the metrics is presented for the first time and the relation between the resolution of numerical schemes and the stretching ratio of grids is discussed. Analysis shows that for smooth varying grids, these characteristics can be generally preserved after the coordinate transformation. Numerical tests also validate our conclusions.

Keywords

Finite difference methodnonuniform gridscoordinate transformationFourier analysis

MSC classification

Secondary: 65N06: Finite difference methods 65N22: Solution of discretized equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 1012 - 1034
Copyright
Copyright © Global-Science Press 2017 

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