A numerical method for solving viscoelastic flows: UCM model

Author(s)

Dayene Miralha de Carvalho

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2004-05-03

Examining board members

Murilo Francisco Tomé; Rosário Elida Suman Bretas; José Alberto Cuminato

• Advisor: Murilo Francisco Tomé

Abstract

In this work a numerical technique for solving viscoelastic flows governed by the upperconvected Maxwell constitutive equation is developed. The governing equations for a Maxwell fluid and boundary conditions for two-dimensional free surface flows using cartesian coordenates are presented. The equations are solved by using the finite difference method on a staggered grid. A new formulation is developed for the computation of the non-Newtonian tensor on rigid boundaries and on free surfaces the full free surface stress conditions are employed. Numerical results demonstrating the convergence of the numerical method are given. In addition, numerical results showing that the numerical method introduced is capable of simulating viscoelastic flows are presented. In particular, the following problems are simulated: jet buckling, extrudate swell and impacting drop. (AU)