Simulation of viscous 2D‐planar cylindrical geometry deformation using DR‐BEM

Abstract

In this paper, a novel boundary element formulation for the deformation of a viscous 2D‐planar cylindrical geometry, immersed in a different viscous fluid and moving towards a rigid wall, is proposed for moderate Reynolds number, considering surface tension effects. The boundary integral formulation for Stokes flow inside and outside the geometry is represented in terms of a combined distribution of a single‐layer and a double‐layer potential of Green functions over the geometry surface. Additionally, non‐linear terms describing effects absent in pure Stokes flow, such as the time derivative of the velocity and inertia, are included. These effects lead to the appearance of domain integrals. Traditional dual reciprocity is applied in order to approximate these domain integrals by a series of particular solutions which are then transformed into boundary integrals. Augmented thin‐plate splines, i.e. r²log(r), plus three additional linear terms from a Pascal triangle expansion were chosen for the dual reciprocity approximation. In order to avoid the discretization of the rigid wall, and using the fact that the velocity on the wall must vanish due to the no‐slip condition, the fundamental solution was modified with a combination of image singularities including an image Stokeslet, a potential dipole and a Stokes‐doublet.

Citation

Hernandez, J.P., Osswald, T.A. and Weiss, D.A. (2003), "Simulation of viscous 2D‐planar cylindrical geometry deformation using DR‐BEM", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 13 No. 6, pp. 698-719. https://doi.org/10.1108/09615530310498385