Lagrangian Concepts for the Numerical Analysis of Viscoelastic Flow

Abstract

The last ten years has seen a steady increase in work on the numerical analysis of the flows of viscoelastic fluids. An excellent account of the status of the field as of 1983 can be found in the monograph by Crochet, Davies & Walters [1]. This surge of activity is driven by the ever increasing availability of computing power, and by the coincident development of constitutive equations which appear to describe qualitatively and sometimes quantitatively the known phenomena of viscoelasticity in fluids. This is not to say that a single equation has now gained acceptance by rheologists, and that work on constitutive theory will now subside. To be specific, for polymeric fluids a handful of constitutive equations are now regarded as appropriate for the analysis of flow problems. Indeed, one of the principal aims of the numerical work is to provide a means for comparing the predictions of these theories. One can regard computer simulation as an adjunct to the theoretical, analytical and experimental methods which have previously been brought to bear on the problem of polymer rheology.KeywordsViscoelastic FluidDeborah NumberWeissenberg NumberMaxwell FluidViscoelastic FlowThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.