A Numerical Method For Solving The Oldroyd-B Model For 3d Free Surface Flows

Abstract

This work presents a numerical method for solving three-dimensional viscoelastic
free surface flows governed by the Oldroyd-B constitutive equation. It is an extension to three
dimensions of the technique introduced by Tom´e et al.1 The governing equations are solved by
a finite difference method on a 3D-staggered grid. Marker particles are employed to describe
the fluid providing the visualization and the location of the fluid free surface. As currently implemented,
the numerical method presented in this work can simulate three-dimensional free
surface flows of an Oldroyd-B fluid. The numerical technique presented in this paper is validated
by using an exact solution of the flow of an Oldroyd-B fluid inside a pipe. Numerical
simulation of the extrudated swell is given.