Symmetric Factorization of the Conformation Tensor in Viscoelastic Fluid Models

Authors

Nusret Balci, University of Minnesota Twin Cities
Becca Thomases, University of Minnesota Twin CitiesFollow
Michael Renardy, University of Minnesota Twin Cities
Charles R. Doering, University of Minnesota Twin Cities

Document Type

Article

Publication Date

6-1-2011

Publication Title

Journal of Non-Newtonian Fluid Mechanics

Abstract

The positive-definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.

Keywords

Direct numerical simulations, FENE-P, Numerical methods, Oldroyd-B, Viscoelastic fluid models

Volume

166

Issue

11

First Page

546

Last Page

553

DOI

10.1016/j.jnnfm.2011.02.008

ISSN

03770257

Comments

Archived as published.

Recommended Citation

Balci, Nusret; Thomases, Becca; Renardy, Michael; and Doering, Charles R., "Symmetric Factorization of the Conformation Tensor in Viscoelastic Fluid Models" (2011). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/170