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

SOFÍA SOLEDAD SARRAF; EZEQUIEL JOSÉ LÓPEZ; GUSTAVO ADOLFO RÍOS RODRÍGUEZ; JORGE D'ELÍA

MATEMATICA APLICADA E COMPUTACIONAL

SOC BRASILEIRA MATEMATICA APLICADA & COMPUTACIONAL

Año: 2014 vol. 33 p. 63 - 80

0101-8205

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.