Applied Mathematics and Mechanics

, Volume 25, Issue 1, pp 59–72 | Cite as

Unsteady/steady numerical simulation of three-dimensional incompressible Navier-Stokes equations on artificial compressibility

  • Wen Gong-bi
  • Chen Zuo-bin


A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.

Key words

incompressible Navier-Stokes equation numerical simulation artificial compressibility central and upwind difference scheme mixed algorithm flow over a prolate spheroid steady/unsteady flow 

Chinese Library Classification


2000 Mathematics Subject Classification

91A13 91B50 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2004

Authors and Affiliations

  • Wen Gong-bi
    • 1
  • Chen Zuo-bin
    • 2
  1. 1.The Department Mechanics and Engineering Science, State Key Laboratory for Turbulence and Complicated System ResearchPeking UniversityBeijingP. R China
  2. 2.China Aerodynamics Research and Development CenterSichuanP. R. China

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