An approach for choosing discretization schemes and grid size based on the convection-diffusion equation

doi:10.1007/s10483-018-2341-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (6): 877-890.doi: https://doi.org/10.1007/s10483-018-2341-9

An approach for choosing discretization schemes and grid size based on the convection-diffusion equation

Lin ZHOU, Zhenghong GAO, Yuan GAO

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2017-09-28 修回日期:2018-01-19 出版日期:2018-06-01 发布日期:2018-06-01
通讯作者: Zhenghong GAO, E-mail:zgao@nwpu.edu.cn E-mail:zgao@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11372254)

An approach for choosing discretization schemes and grid size based on the convection-diffusion equation

Lin ZHOU, Zhenghong GAO, Yuan GAO

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2017-09-28 Revised:2018-01-19 Online:2018-06-01 Published:2018-06-01
Contact: Zhenghong GAO E-mail:zgao@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11372254)

摘要/Abstract

摘要：

A new approach for selecting proper discretization schemes and grid size is presented. This method is based on the convection-diffusion equation and can provide insight for the Navier-Stokes equation. The approach mainly addresses two aspects, i.e., the practical accuracy of diffusion term discretization and the behavior of high wavenumber disturbances. Two criteria are included in this approach. First, numerical diffusion should not affect the theoretical diffusion accuracy near the length scales of interest. This is achieved by requiring numerical diffusion to be smaller than the diffusion discretization error. Second, high wavenumber modes that are much smaller than the length scales of interest should not be amplified. These two criteria provide a range of suitable scheme combinations for convective flux and diffusive flux and an ideal interval for grid spacing. The effects of time discretization on these criteria are briefly discussed.

关键词: composite materials mechanics, interphase, interface element, diffusion term accuracy, high wavenumber mode, convection-diffusion equation, cell Reynolds number, scheme selection

Abstract:

Key words: composite materials mechanics, interphase, interface element, diffusion term accuracy, scheme selection, convection-diffusion equation, high wavenumber mode, cell Reynolds number

中图分类号:

76G25
76M20

Lin ZHOU, Zhenghong GAO, Yuan GAO. An approach for choosing discretization schemes and grid size based on the convection-diffusion equation[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(6): 877-890.

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An approach for choosing discretization schemes and grid size based on the convection-diffusion equation

An approach for choosing discretization schemes and grid size based on the convection-diffusion equation

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