New Formulation for Stress Calculation: Application to Viscoelastic Flow in a T-Junction

Abstract

In this study, a new formulation is proposed for the calculation of stress components at control-volume faces, within the context of cell-centered finite-volume methods which have the stress tensor as one of the main dependent variables. Test case results from calculations with viscoelastic fluids flowing through a T-junction demonstrate the merits of the method. Previous formulations for stress interpolation yielded results that would depend on the time-step value employed, even when calculating steady-state problems. We have removed this inconsistency by devising an improved method that gives results independent of the time step and that in addition is more robust, with a wider range of allowable Deborah numbers. A FENE-CR constitutive model is used to replicate the known viscoelastic nature of blood, and results are given for varying fluid elasticities, at values of Reynolds number and extraction ratio typical of hemodynamic applications.

Acknowledgments

Financial support by Fundação para a Ciência e a Tecnologia (FCT, Portugal) through Ph.D. grant SFRH/BD/18062/2004 (M.H.H.) and project PTDC/EQU-FTT/71800/2006 (M.A.A.) is gratefully acknowledged. P.J.O. also acknowledges a sabbatical leave provided by Universidade da Beira Interior.