Stokes flow around an asymmetric channel divider; a computational approachusing MATLAB

While computational methods for solving Stokes-flow problems have existed f or some time, these have depended on specialized codes developed specifical ly, for this type of problem. This work shows how to combine traditional ap plied mathematics and a modern over-the-counter software package MATLAB to solve and study Stokes flow in a channel with a splitter plate. Specificall y exact unidirectional flow solutions are used as a basis for choosing boun dary conditions for MATLAB to anticipate the boundary conditions of a Stoke s flow. A method for selecting zeroth and first-order approximate boundary conditions is presented, along with a suggestion for finding a second-order approximation. It is also shown that small errors made in choosing the app roximate boundary conditions do not grow as one moves away from the boundar y into the interior of the flow. Finally several computational examples usi ng this approach are presented.