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Preconditioned pseudo-compressibility methods for incompressible Navier-Stokes equations

中国科学：物理学、力学、天文学英文版 2010年第11期53卷 2090-2102页

作者： QIAN ZhanSen ,ZHANG JingBai & LI ChunXuan School of Aeronautics Science and Engineering,Beihang University,Beijing 100191,China School of Aeronautics Science and Engineering Beihang University Beijing China

This paper investigates the pseudo-compressibility method for the incompressible Navier-Stokes equations and the preconditioning technique for accelerating the time marching for stiff hyperbolic equations,and derives and presents the eigenvalues and eigenvectors of the Jacobian matrix of the preconditioned pseudo-compressible Navier-Stokes equations in generally cur-vilinear *** on the finite difference discretization the cored for efficiently solving incompressible flows numerically is *** reliability of the procedures is demonstrated by the application to the inviscid flow past a circular cylinder,the laminar flow over a flat plate,and steady low Reynolds number viscous incompressible flows past a circular *** is found that the solutions to the present algorithm are in good agreement with the exact solutions or experimental *** effects of the pseudo-compressibility factor and the parameter brought by preconditioning in convergence characteristics of the solution are investigated *** results show that the upwind Roe’s scheme is superior to the second order central scheme,that the convergence rate of the pseudo-compressibility method can be effectively improved by preconditioning and that the self-adaptive pseudo-compressibility factor can modify the numerical convergence rate significantly compared to the constant form,without doing artificial tuning depending on the specific flow *** validation is also performed by numerical simulations of unsteady low Reynolds number viscous incompressible flows past a circular *** results are also found in good agreement with the existing numerical results or experimental data.

关键词： pseudo-compressibility method preconditioning upwind scheme incompressible flow Navier-Stokes equations

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