A Galerkin Boundary Element Method for Stokes Flow Around Bodies with Sharp Corners and Edges

Abstract

In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around closed rigid bodies with sharp corners and edges is numerically solved using a Galerkin scheme applied to a modified 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)). As a numerical example, the creeping steady flow around the unit cube considering different orientations with respect to the unperturbed fluid velocity, covering issues on the surface traction exponents close to the edges and vertices and compared against semi-analytical computations.