A Numerical Technique For Simulating Viscoelastic Free Surface Flows Using The K-Bkz Integral Constitutive Equation

Abstract

This work presents a numerical technique for simulating viscoelastic free surface flows governed by the K-BKZ integral constitutive equation. The numerical method solves the governing equations using the finite difference method on a staggered grid. The equation of motion is integrated by the GENSMAC methodology. The fluid surface is modeled by the marker-and-cell method which provides the visualization and the location of the fluid free surface. The full free surface stress conditions are employed. The Finger tensor is computed using the ideas of the deformation fields method. The integrand of the integral constitutive equation is approximated by a linear piecewise function which is integrated exactly and the transport term of the Finger strain tensor is approximated by a high order upwind scheme. Numerical results showing the convergence of the numerical method developed in this work for the flow in a two-dimensional channel are presented. In addition, the simulations of the flow through a planar 4:1 contraction and jet buckling are given.