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

doi:10.4208/eajam.281120.060421

	Fixing the Residual Flattening of an Upwind Compact Scheme for Steady Incompressible Flows in Enclosed Domains
	Wang, Yunchu ; Yuan, Li 1
刊名	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
	2021-11-01
卷号	11 期号:4 页码:708-731
关键词	Incompressible Navier-Stokes equations artificial compressibility upwind compact difference convergence enclosed domain
ISSN号	2079-7362
DOI	10.4208/eajam.281120.060421
英文摘要	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.
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
语种	英语
出版者	GLOBAL SCIENCE PRESS
WOS记录号	WOS:000750799600004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59947]
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.