Galerkin boundary elements for the computation of the surface tractions in exterior Stokes flows

D'ELÍA, JORGE; BATTAGLIA, LAURA; CARDONA ALBERTO; STORTI MARIO; GUSTAVO A. RÍOS RODRIGUEZ

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME

ASME-AMER SOC MECHANICAL ENG

Lugar: New York; Año: 2014

0098-2202

In the computation of a three-dimensional steady creeping flow arounda rigid body, the total body force and torque are well predicted usinga Boundary Integral Equation (BIE) with a single concentrated pairStokesletrotlet located at an interior point of the body. However, thedistribution of surface tractions are seldom considered. Then, acompleted indirect velocity BIE of Fredholm type and second-kind isemployed for the computation of the pointwise tractions, and it isnumerically solved by using either collocation or 1 Galerkin weightingprocedures over flat triangles. In the Galerkin case, a full numericalquadrature is proposed in order to handle the weak singularity of thetensor kernels, which is an extension for fluid engineering of ageneral framework (Taylor, D. J., 2003, "Accurate and efficientnumerical integration of weakly singulars integrals in Galerkin EFIEsolutions", IEEE Trans. on Antennas and Propag., 51(7):1630-1637).Several numerical simulations of steady creeping flow around closedbodies are presented, where results compare well with semi-analyticaland finite-element solutions, showing the ability of the method forobtaining the viscous drag and capturing the singular behavior of thesurface tractions close to edges and corners. Also, deliberatelyintricate geometries are considered.