Boundary Element Simulation of Axisymmetric Viscous Creeping Flows under Gravity in Free Surface Domains

Abstract

An indirect boundary element method is proposed for the numerical solution of the Stokes equations in the axisymmetric case with Dirichlet and Neumann boundary conditions, which correspond to the velocity given on a part of the boundary and to the traction given on the other part. The method is described as applied to quasi-steady viscous creeping flows under gravity in regions bounded by a free surface and solid walls. A viscous fluid drop spreading over a hydrophobic horizontal surface is considered as an example. It is shown that the use of no-slip conditions ensure that the results have approximation convergence and satisfy the mass and energy conservation laws.