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

D'ELIA, J.; LAURA BATTAGLIA; ALBERTO CARDONA; MARIO STORTI; GUSTAVO RIOS RODRIGUEZ

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME

ASME-AMER SOC MECHANICAL ENG

Lugar: New York; Año: 2014 vol. 136

0098-2202

In the computation of a three?dimensional steady creeping flow around a rigid body, the total body force and torque are well predicted using a Boundary Integral Equation (BIE) with a single concentrated pair Stokeslet- rotlet located at an interior point of the body. However, the distribution of surface tractions are seldom considered. Then, a completed indirect velocity BIE of Fredholm type and second-kind is employed for the computation of the pointwise tractions, and it is numerically solved by using either collocation or Galerkin weighting procedures over flat triangles. In the Galerkin case, a full numerical quadrature is proposed in order to handle the weak singularity of the tensor kernels, which is an extension for fluid engineering of a general framework (Taylor, D. J., 2003,  Accurate and efficient numerical integration of weakly singulars integrals in Galerkin EFIE solutions, IEEE Trans. on Antennas and Propag., 51(7):1630-1637). Several numerical simulations of steady creeping flow around closed bodies are presented, where results compare well with semi-analytical and finite-element solutions, showing the ability of the method for obtaining the viscous drag and capturing the singular behavior of the surface tractions close to edges and corners. Also, deliberately intricate geometries are considered.