IJPAM: Volume 30, No. 2 (2006)
AN OSCILLATING PLANE WALL: ANALYTICAL
SOLUTION VS. NUMERICAL SOLUTION
Department of Informatics
Athens University of Economics and Business
76, Patision Str., Athens, 10434, GREECE
Abstract.In this paper, the numerical solution of an incompressible, viscous, electrically conducting, fluid stream past an oscillating plane wall, is being compared with the analytical solutions presented by Poria et al [#!10!#]. In the beginning the basic equation, governing the motion of such a flow is expressed in non-dimensional form. Then we attempt to find possible analytical solutions for the velocity field and compute them separately with appropriate boundary and initial conditions. It is shown that this equation admits of two solutions that satisfy the respective sets of boundary and initial conditions. Then we try to solve the same equation expressed in non-dimensional form numerically.
The numerical calculations have been performed by a finite difference method
using the well-known Crank-Nicholson implicit scheme. The results, showing
the development of the velocity field in time for different values of a
magnetic parameter, are presented graphically and discussed.
Received: June 15, 2006
AMS Subject Classification: 65C20
Key Words and Phrases: MHD fluid flow, oscillating plane wall, Crank-Nicholson implicit scheme
Source: International Journal of Pure and Applied Mathematics