An accurate boundary-element method for Stokes flow in partially covered cavities

The two-dimensional flow of a viscous fluid over an etched hole is computed with a boundary-element method. The etch-hole geometry contains sharp corners at which the solution of the traction boundary-integral equation is singular. Therefore, only the regular part of the solution is computed with the boundary-element method, using a singularity-subtraction method, and the singular part of the solution is added. However, there are regions in which these regular and singular parts are of almost equal magnitude, but different in sign. To avoid the subtraction and addition of large quantities where quantities of smaller order are computed a domain-decomposition technique is introduced. We show that the accuracy indeed increases by the described techniques. After extrapolation the results for a rectangular geometry agree very well with results obtained earlier with a semi-analytical method. A new integral formulation is derived for the stream function in the form of a boundary integral over the velocity and shear-stress components. Finally we show some results for arbitrary etch holes.