Application of Boundary Collocation Method in Fluid Mechanics
by
Anna Kucaba-Piêtal
Department of Fluid Mechanics and Aerodynamics, Rzeszow University of Technology, Rzeszow, W.Pola 2, Poland

Boundary methods are usually understood as numerical procedures which require the use of trial functions satisfying the differential equation and which reduce the boundary conditions to an approximate form. There are two main possibilities to formulate boundary methods; one is based on the use of the boundary integral equations (see for example (1)) and the other one and the second one, on the use of some systems of trial functions. In the latter approach this system must be complete. The boundary collocation method (BCM) belongs to the second version of the boundary method and is the most primitive version of this method. The biggest advantage of this method in comparison with the others ones( Finite Element Methods, Finite Difference Methods) is that for slightly more complicated regions it requires less work. Disadvantages if the boundary collocation method is that it is applicable only for linear problems.

The Stokes equations are linear and in fluid mechanics are used to describe creeping flows which appear in microhydrodynamics and biomechanics. These flows have general application in colloids, suspension rheology, aerosols and microfabricated fluid systems (i.e. pumps, valves, microchannels, computer chips). The aim of the presentation is to present the boundary collocation method for solving some problems of microhydrodynamics. We focus on the hydrodynamic interaction between a wall and a sphere moving axisymetrically in fluid towards the flat wall. This problem occurs in microdevices and in human joins, too. To model such situation the Stokes approach is considered, moreover Newtonian and non-Newtonian model of the fluid is taken into account. The numerical results will be presented at the Conference.

[1] GANATOS P., WEINBAUM S., PFEFFER R., 1980, A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries, J. Fluid Mech. Vol. 99, pp 739- 753 [2] KO£ODZIEJ J. A., 1987, Review of application of boundary collocation methods in mechanics of continuous media, SM Archives 12/4 , pp. 187-231 [3] KUCABA-PIÊTAL A., 1999, Flow past a sphere moving towards a wall in micropolar fluid, J. Theor. Appl. Mech. 2, vol 37, pp. 301-318

Date received: January 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeb-63.