Boundary Element Grid Optimization for Stokes Flow With Corner Singularities

Abstract

The accuracy of boundary-element methods for computing Stokes flow past boundaries with sharp corners where singularities occur is discussed. To resolve the singular behavior, a graded mesh of boundary elements whose length increases in a geometrical fashion with respect to distance from the corners according to a prescribed stretch ratio is used. Numerical results for two-dimensional Stokes flow past bodies with polygonal shapes reveal the existence of an optimal value of the stretch ratio for best accuracy in the computation of the force and torque. When the optimal value is used, fast convergence is achieved with respect to the number of boundary elements.