Galerkin Boundary Integral Equations Applied to Three Dimensional Stokes Flows

Abstract

In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around closed rigid bodies is numerically solved using a Galerkin scheme applied to the Power-Miranda boundary integral equation. The related double surface integrals that account the pairwise interaction
among all boundary elements are quadruple and they are computed on flat simplex triangles using the scheme proposed by Taylor (D. J. Taylor, IEEE Trans. on Antennas and Propagation, 51(7):1630–1637 (2003)). Numerical examples include the creeping steady flow around the unit sphere and the unit cube, covering issues on the convergence under mesh refinement of the numerical solution, stability under small mesh perturbations and indifference of the drag force to the direction of the incoming velocity relative to a center line of the body.