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

作　　者：Benwen LI Shangshang CHEN 

机构地区：[1]Institute of Thermal Engineering, School of Energy and Power Engineering,Dalian University of Technology [2]Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education),Northeastern University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第8期1073-1090,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.51176026);the Fundamental Research Funds for the Central Universities(No.DUT14RC(3)029)

摘　　要：An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar 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 Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary 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 be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar 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 Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary 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 be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.

关 键 词：incompressible Navier-Stokes equation domain decomposition influencematrix technique Chebyshev collocation spectral method 

分 类 号：O175[理学—数学]