Numerical-simulation of Viscoelastic Flow - a Review

Abstract It is evident that a major effort has been accomplished over the last ten years toward the development of numerical methods for solving viscoelatic flow. The problem was clearly much harder than expected. Several extensive reviews have been devoted to a detailed account of the difficulties encountered in reaching moderate values of the Weissenberg number. The numerical and analytical work undertaken in parallel by several research groups has led to some important conclusions which paved the way for recent promising development. First, numerical algorithms for solving highly nonlinear advective problems must be used with the greatest carefulness. When spurious solutions or unexpected effects such as limit points arise in numerical simulations, we have learned to question the validity of the numerical method as well as that of the constitutive equation. Typically, successive failures of numerical calculations with the Maxwell model at low values of We have often been attributed to its singular beha...