Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T02:29:01.957Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-Dimensional Incompressible Viscous Flow Simulation Using Velocity-Vorticity Dual Reciprocity Boundary Element Method

Published online by Cambridge University Press:  05 May 2011

T. I. Eldho  and
D. L. Young
T. I. Eldho*
Affiliation:
Department of Civil Engineering, Indian Institute of Technology, Bombay, Mumbai, India - 400 076
D. L. Young*
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Assistant Professor
**Professor
Get access

Abstract

This paper describes a computational model based on the dual reciprocity boundary element method (DRBEM) for the solution of two-dimensional incompressible viscous flow problems. The model is based on the Navier-Stokes equations in velocity-vorticity variables. The model includes the solution of vorticity transport equation for vorticity whose solenoidal vorticity components are obtained by solving Poisson equations involving the velocity and vorticity components. Both the Poisson equations and the vorticity transport equations are solved iteratively using DRBEM and combined to determine the velocity and vorticity vectors. In DRBEM, all source terms, advective terms and time dependent terms are converted into boundary integrals and hence the computational domain of the problem reduces by one. Internal points are considered wherever solution is required. The model has been applied to simulate two-dimensional incompressible viscous flow problems with low Reynolds (Re) number in a typical square cavity. Results are obtained and compared with other models. The DRBEM model has been found to be reasonable and satisfactory.

Keywords

Navier-Stokes equationsVelocity-vorticityDual reciprocity boundary element method.
Type
Articles
Information
Journal of Mechanics , Volume 20 , Issue 3 , September 2004 , pp. 177 - 185
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anderson, D. A., Tannehill, J. C. and Fletcher, R. H., Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, New York (1984).Google Scholar
2.Gunzaburger, M. D., “Finite Element Theory and Application,” Proc. of ICASE/NASA Langly Workshop, Dwoyer, D. L., Hussaini, M. Y., and Voigt, R. G., eds., Springer-Verlag, New York (1987).Google Scholar
3.Power, H. and Wrobel, L. C., Boundary Integral Methods in Fluid Mechanics, Computational Mechanics Publications, Southampton (1995).Google Scholar
4.Banerjee, P. K., The Boundary Element Methods in Engineering, McGraw-Hill, New York (1994).Google Scholar
5.Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., Boundary Element Techniques — Theory and Applications in Engineering, Springer-Verlag, Berlin (1984).CrossRefGoogle Scholar
6.Partridge, P. W., Brebbia, C. A. and Wrobel, L. C., The Dual Reciprocity Boundary Element Method, Computational Mechanics Publications, Southampton, Elsevier, London (1992).Google Scholar
7.Nardini, D. and Brebbia, C. A., “A New Approach to Free Vibration Analysis Using Boundary Elements,” Boundary Element Methods in Engineering, Computational Mechanics Publications, Southampton, Springer-Verlag, Berlin (1982).Google Scholar
8.Eldho, T. I., Young, D. L., “Solution of Stokes Flow Problem Using Dual Reciprocity Boundary Element Method,” J. Chinese Institute of Engineers, 24(2), pp. 141–150(2001).CrossRefGoogle Scholar
9.Liggett, J. A., Fluid Mechanics, McGraw-Hill Inc., New York (1994).Google Scholar
10.Burggraf, O. R., “Analytical and Numerical Studies of the Structure of Steady Separated Flows,” J. FluidMech., 24 (1), pp. 113–151 (1966).CrossRefGoogle Scholar
11.Young, D. L. and Lin, Q. H. “Application of Finite Element Method to 2-D Flows,” Proc. 3rd Nat. Conf. Hydraulic Eng., Taipei, pp. 223–242 (1986).Google Scholar
12.Young, D. L. and Yang, S. K., “Simulation of Two-Dimensional Steady Stokes Flows by the Velocity-Vorticity Boundary Element Method,” Proc. 20th Nat. Mechanics Conference, Taipei, pp. 422–429 (1996).Google Scholar
13.Ghia, U., Ghia, K. N. and Shin, C. T., “High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,” J. Comput. Phys., 48, pp. 387–411 (1982).CrossRefGoogle Scholar
14.Young, D. L., Yang, S. K. and Eldho, T. I., “The Solution of the Navier-Stokes Equations in Velocity-Vorticty Form Using Eulerian-Lagrangian Boundary Element Method,” Int. J. Numer. Meth. Fluids, 34, pp. 627–650 (2000).3.0.CO;2-J>CrossRefGoogle Scholar