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A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations
Tian ZF; Liang X(梁贤); Yu PX; Tian, ZF (reprint author), Fudan Univ, Dept Engn Sci & Mech, Shanghai 200433, Peoples R China
Source PublicationInternational Journal for Numerical Methods in Engineering
2011
Volume88Issue:6Pages:511-532
ISSN0029-5981
AbstractOn the basis of the projection method, a higher order compact finite difference algorithm, which possesses a good spatial behavior, is developed for solving the 2D unsteady incompressible Navier-Stokes equations in primitive variable. The present method is established on a staggered grid system and is at least third-order accurate in space. A third-order accurate upwind compact difference approximation is used to discretize the non-linear convective terms, a fourth-order symmetrical compact difference approximation is used to discretize the viscous terms, and a fourth-order compact difference approximation on a cell-centered mesh is used to discretize the first derivatives in the continuity equation. The pressure Poisson equation is approximated using a fourth-order compact difference scheme constructed currently on the nine-point 2D stencil. New fourth-order compact difference schemes for explicit computing of the pressure gradient are also developed on the nine-point 2D stencil. For the assessment of the effectiveness and accuracy of the method, particularly its spatial behavior, a problem with analytical solution and another one with a steep gradient are numerically solved. Finally, steady and unsteady solutions for the lid-driven cavity flow are also used to assess the efficiency of this algorithm. Copyright (C) 2011 John Wiley & Sons, Ltd.
KeywordNavier-stokes Equations Higher Order Compact Finite Difference Primitive Variable Projection Method Spectral-projection Method Numerical-solution Flow Calculations Cavity Flow Scheme 4th-order Formulation
Subject AreaEngineering ; Mathematics
DOI10.1002/nme.3184
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000296262500001
WOS KeywordSPECTRAL-PROJECTION METHOD ; NUMERICAL-SOLUTION ; FLOW CALCULATIONS ; CAVITY FLOW ; SCHEME ; 4TH-ORDER ; FORMULATION
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
Funding OrganizationThis work was supported in part by the National Natural Science Foundation of China under Grants 10972058 and 10662006, Research Fund for the Doctoral Program of Higher Education of China, the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, People's Republic of China, China Postdoctoral Science Foundation, and the High Performance Computing Foundation of China under Grants 99107 and 00108.
DepartmentLHD可压缩湍流
Classification一类
Citation statistics
Cited Times:38[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/45165
Collection高温气体动力学国家重点实验室
Corresponding AuthorTian, ZF (reprint author), Fudan Univ, Dept Engn Sci & Mech, Shanghai 200433, Peoples R China
Recommended Citation
GB/T 7714
Tian ZF,Liang X,Yu PX,et al. A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations[J]. International Journal for Numerical Methods in Engineering,2011,88(6):511-532.
APA Tian ZF,梁贤,Yu PX,&Tian, ZF .(2011).A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations.International Journal for Numerical Methods in Engineering,88(6),511-532.
MLA Tian ZF,et al."A higher order compact finite difference algorithm for solving the incompressible Navier-Stokes equations".International Journal for Numerical Methods in Engineering 88.6(2011):511-532.
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