Validation of a Galerkin technique on a boundary integral equation for creeping flow around a torus

Abstract

A validation of the numerical solution for the steady and axisymmetric creeping flow around a three-dimensional torus is presented. This solution is obtained by means of the Boundary Element Method. Both, a Galerkin weighting technique and collocation to the centroid of the elements are employed. The curve of the viscous drag force as a function of the diameter of the torus relative to its thickness is compared against a semi-analytical solution and laboratory experimental measurements taken from the literature. The semi-analytical solution, as it is known for this kind of geometry, involves the Legendre functions of first and second kind of order one and semi-integer degrees, also called toroidal harmonics.