IJPAM: Volume 13, No. 3 (2004)

EFFICIENT NUMERICAL SOLUTION OF
3D INCOMPRESSIBLE VISCOUS
NAVIER-STOKES EQUATIONS

Salwa K. Abd-El-Hafiz$^1$, Gamal A.F. Ismail$^2$, Berlant S. Matit$^3$
$^1$Engineering Mathematics Department
Faculty of Engineering
Cairo University
Giza 12211, EGYPT
e-mail: salwahafiz@link.net
$^{2,3}$Department of Applied Mathematics
Women's College
Ain Shams University
Cairo, EGYPT


Abstract.This paper focuses on the numerical solution of the three dimensional incompressible viscous Navier-Stokes equations. Using the vorticity-vector potential approach, a technique for the solution of the Navier-Stokes equations is presented. The parabolic vorticity transport equation and the elliptic Poisson equation are discretized in a collocated Cartesian grid. Using the finite difference method, an iterative technique for the solution of the three dimensional Poisson equation is presented. With respect to the vorticity transport equation, the explicit Euler method is used. In addition, we study the boundary conditions as well as the stability of the numerical techniques. Finally, we present our time-marching algorithm. The correctness of the algorithm is demonstrated on the model problem of the lid-driven cavity in three-dimensional space.

Received: March 28, 2004

AMS Subject Classification: 35Q30, 65M06, 65M12

Key Words and Phrases: finite difference, elliptic Poisson equation, parabolic vorticity transport equation, lid-driven cavity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 3