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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1073–1090 | Cite as

Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations

  • Benwen LiEmail author
  • Shangshang Chen
Article
  • 143 Downloads

Abstract

An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and incompressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangular sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method (CSM) is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neumann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet boundary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison between the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.

Keywords

incompressible Navier-Stokes equation domain decomposition influence matrix technique Chebyshev collocation spectral method 

Chinese Library Classification

O241.82 O357.1 

2010 Mathematics Subject Classification

74S25 76D05 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute of Thermal Engineering, School of Energy and Power EngineeringDalian University of TechnologyDalian, Liaoning ProvinceChina
  2. 2.Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education)Northeastern UniversityShenyangChina

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