A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations

Sun Jian'an; Zhu Zhengyou

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(12): 1259-1266

Sun Jian'an, Zhu Zhengyou. A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1259-1266.

Citation:

Sun Jian'an, Zhu Zhengyou. A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1259-1266.

Citation:

Sun Jian'an, Zhu Zhengyou. A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1259-1266.

PDF( 340 KB)

A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations

Sun Jian'an¹,
Zhu Zhengyou²

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;

Received Date: 1998-01-06
Rev Recd Date: 1999-04-21
Publish Date: 1999-12-15

Abstract

Abstract

Differential quadrature method(DQM)is able to obtain highly accurate numerical solutions of differential equations just using a few grid points.But using purely differential quadrature method, good numerical solutions 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 incompressible 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.
- numerical method,
- differential quadrature method,
- Navier-Stokes equations

FullText(HTML)

References(10)

References

[1]	Bellman R, Casti J. Differential quadrature and long-term integration[J]. J Math Anal Appl,1971,34(2):235～238.
[2]	Bellman R, Kashef B G, Casti J. Differential quadrature: a technique for the rapid solution of non～linear partial differential equations[J]. J Comput Phys,1972,10(1):40～52.
[3]	Bert C W, Malik M. Differential quadrature method in computational mechanics: a review[J]. Appl Mech Rev,1996,49(1):1～27.
[4]	Shu C, Richards B E. Application of generalized differential quadrature to solve two-dimentional incompressible Navier-Stokes equations[J]. Int J Numer Methods Fluids,1992,15(7):791～798.
[5]	Chu C, Richards B F. Parallel simulation of incompressible viscous flows by generalized differential quadrature[J]. Comput Syst Eng,1992,3(1-4):271～281.
[6]	Striz A G, Chen W L. Application of the differential quadrature method to the driven cavity problem[J]. Int J Non-Linear Mech,1994,29(5):665～670.
[7]	Chia U, Chia K N, Shin C T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. J Comput Phys,1982,48(2):387～411.
[8]	Kawaguti M. Numerical solution of the Navier-Stokes equations for the flow in a two-dimensional cavity[J]. J Phys Soc Japan,1961,16(8):2307～2315.
[9]	Burggraf O R. Analytical and numerical studies of the structure of steady separated flow[J]. J Fluid Mech,1966,24(1):113～151.
[10]	Prosnak W J, Kosma Z J. On a new method for numerical solution of the Navier-Stokes equations[J]. Acta Mechanica,1991,89(1):45～63.