Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations

被引:62
作者
Shah, Abdullah [1 ,2 ]
Yuan, Li [1 ]
Khan, Aftab [2 ]
机构
[1] Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] COMSATS Inst Informat Technol, Dept Math, Islamabad, Pakistan
关键词
Incompressible Navier-Stokes equation; Artificial compressibility method; Upwind compact finite difference; Flux-difference splitting; Dual-time stepping; Kovasznay flow problem; Oscillating plate; Taylor's decaying vortices; Doubly periodic shear layer; FLUID; FLOW; FORMULATION;
D O I
10.1016/j.amc.2009.10.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This article presents a time-accurate numerical method using high-order accurate compact finite difference scheme for the incompressible Navier-Stokes equations. The method relies on the artificial compressibility formulation, which endows the governing equations a hyperbolic-parabolic nature. The convective terms are discretized with a third-order upwind compact scheme based on flux-difference splitting, and the viscous terms are approximated with a fourth-order central compact scheme. Dual-time stepping is implemented for time-accurate calculation in conjunction with Beam-Warming approximate factorization scheme. The present compact scheme is compared with an established non-compact scheme via analysis in a model equation and numerical tests in four benchmark flow problems. Comparisons demonstrate that the present third-order upwind compact scheme is more accurate than the non-compact scheme while having the same computational cost as the latter. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:3201 / 3213
页数:13
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