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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (12): 1358-1366.

• 论文 • 上一篇    下一篇

A MIXTURE DIFFERENTIAL QUADRATURE METHOD FOR SOLVING TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

孙建安1, 朱正佑2,3   

  1. 1. Department of Physics, Northwest Normal University, Lanzhou 730070, P. R. China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    3. Department of Mathematics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:1998-01-06 修回日期:1999-04-21 出版日期:1999-12-18 发布日期:1999-12-18

A MIXTURE DIFFERENTIAL QUADRATURE METHOD FOR SOLVING TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

Sun Jian’an1, Zhu Zhengyou2,3   

  1. 1. Department of Physics, Northwest Normal University, Lanzhou 730070, P. R. China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    3. Department of Mathematics, Shanghai University, Shanghai 200072, P. R. China
  • Received:1998-01-06 Revised:1999-04-21 Online:1999-12-18 Published:1999-12-18

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摘要： Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equation s just using a few grid points.But using purely differential quadrature method,good numerical solution s of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason,in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional in compressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one.Using this scheme and pseudo-time-dependent algorithm,numerical solutions of high Reynolds number flow are obtained with only a few grid points.For example,1:1 and 1:2 driven cavity flows are calculated and good numerical solutions are obtained.

Abstract: Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equation s just using a few grid points.But using purely differential quadrature method,good numerical solution s of two-dimensional incompressible Navier-Stokes equations can be obtained only for low Reynolds number flow and numerical solutions will not be convergent for high Reynolds number flow. For this reason,in this paper a combinative predicting-correcting numerical scheme for solving two-dimensional in compressible Navier-Stokes equations is presented by mixing upwind difference method into differential quadrature one.Using this scheme and pseudo-time-dependent algorithm,numerical solutions of high Reynolds number flow are obtained with only a few grid points.For example,1:1 and 1:2 driven cavity flows are calculated and good numerical solutions are obtained.

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