A Hybrid Finite Element/Finite Difference Algorithm for Compressible/incompressible Viscoelastic Liquids

摘要

A unified formulation is proposed for modelling compressible/incompressible viscoelastic liquids. The pure hyperbolic nature of the model overcomes some of the drawbacks of available models. The most important of these drawbacks is the mixed nature of the resulting systems of equations, with the subsequent consequence of having no general numerical algorithm for the solution. A new non-dimensionalisation procedure is adopted. A hybrid least-squares finite element/finite difference scheme coupled with a Newton-Raphson's algorithm is used to solve the resulting system of equations. The method is used to predict the velocity and stress fields for different Weissenberg numbers for two benchmark problems.