A variational approach for coupled creepingflow problems
Abstract
The majority of the available solutions of the Stokes equations refer to inflow and/or outflow boundary conditions assigned at a given station. In practice, the entrance of a flow field is always the exit of some other flow field, and therefore coupling of two infinite flow regions of different shape is of interest. In coupled creeping flow problems, a singularity arises on the boundaries at the transition point which makes it difficult to attack them by standard techniques. Here, the coupling problem is treated by an approximate analytical method based on a variational principle. This method is flexible enough to deal with a wide range of geometries and allows the introduction of singular terms describing correctly the local behavior of the solution, which makes even a fewterm approximation accurate. The variational approach is applied to an example case of an infinite array of parallel ducts (of which only one is depicted) discharging in free space.
 Publication:

Twelfth Canadian Congress of Applied Mechanics
 Pub Date:
 May 1989
 Bibcode:
 1989apme.proc..774L
 Keywords:

 Calculus Of Variations;
 Creep Analysis;
 Plastic Flow;
 Singularity (Mathematics);
 Static Deformation;
 Stokes Flow;
 Boundary Value Problems;
 Coupling;
 Flow Distribution;
 Transition Points;
 Structural Mechanics