Accurate Boundary-Element Method for Stokes Flow in Partially Covered Cavities

摘要

The two-diemensional flow of a viscous fluid over an etched hole is computed with211u001ea boundary-element method. The etch-hole geometry contains sharp corners at which 211u001ethe solution of the traction boundary-integral equation is singular. Therefore, 211u001eonly the regular part of the solution is computed with the boundary-element 211u001emethod, using a singularity-subtraction method, and the singular part of the 211u001esolution is added. However, there are regions in which these regular and singular 211u001eparts are of almost equal magnitude, but differenet in sign. To avoid the 211u001esubtraction and addition of large quantities where quantities of smaller order 211u001eare computed a domain-decomposition technique is introduced. The authors show 211u001ethat the accuracy indeed increases by the described techniques. After 211u001eextrapolation the results for a rectangular geometry agree very well with results 211u001eobtained earlier with a semi-analytical method.