Computation of Large Strain in the Simulation of Memory Fluids

Abstract

Several efforts are currently under way to apply numerical methods to solve for complex flows of viscoelastic fluids in which the constitutive equation is represented as a memory integral. Computationally the integral form is attractive because it avoids the demands for higher order derivatives of field variables imposed by the equivalent differential form, if indeed one exists. The aim of “computational rheology” should be to provide the capability of testing a variety of constitutive hypotheses. This points to the need to be able to handle memory integrals, a computationally complex task. It has recently been shown that a memory integral, finite element formulation of the Maxwell model can be made to work over a range of Deborah numbers comparable to the best results obtained from formulations based on the differential form. During the course of this work it was found that a limitation on the integral form is the accurate computation of large strains. In practice the displacements of a finite number of nodal points are determined by a path integration in the velocity field. It turns out the main difficulty is not in the accurate computation of displacements, but in the way in which stains are computed from them.