Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations
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论文类型：期刊论文
发表时间：2015-08-01
发表刊物：APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
收录刊物：SCIE、EI、CSCD、Scopus
卷号：36
期号：8
页面范围：1073-1090
ISSN号：0253-4827
关键字：incompressible Navier-Stokes equation; domain decomposition; influence matrix technique; Chebyshev collocation spectral method
摘要：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.
发表时间：2015-08-01