Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains

doi:10.4208/eajam.281120.060421

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	Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains
	Wang, Yunchu ; Yuan, Li 1
	2021-11-01
发表期刊	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN	2079-7362
卷号	11 期号:4 页码:708-731
摘要	The iterative convergence of the upwind compact finite difference scheme for the artificial compressibility method [A. Shah et al., A third-order upwind compact scheme on curvilinear meshes for the incompressible Navier-Stokes equations, Commun. Comput. Phys. 5 (2009)] is studied. It turns out that for steady flows in enclosed domains the residuals do not converge to machine zero. The reason is a non-uniqueness of the calculated pressure in the case where Neumann boundary conditions for the pressure are imposed on all boundaries. The problem can be fixed by modifying the derivatives of mass flux obtained from the upwind compact scheme to satisfy the global mass conservation constraint. Numerical tests show that with this modification the scheme converges to machine zero with the original third-order accuracy.
关键词	Incompressible Navier-Stokes equations artificial compressibility upwind compact difference convergence enclosed domain
DOI	10.4208/eajam.281120.060421
收录类别	SCI
语种	英语
资助项目	Natural Science Foundation of China[91641107] ; Natural Science Foundation of China[91852116] ; Natural Science Foundation of China[12071470]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000750799600004
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59948
专题	中国科学院数学与系统科学研究院
通讯作者	Yuan, Li
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, Yunchu,Yuan, Li. Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2021,11(4):708-731.
APA	Wang, Yunchu,&Yuan, Li.(2021).Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,11(4),708-731.
MLA	Wang, Yunchu,et al."Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 11.4(2021):708-731.