Symmetric factorization of the conformation tensor in viscoelastic fluid models

TL;DR

This paper introduces a symmetric factorization approach for the conformation tensor in viscoelastic fluid models, leading to more accurate and stable numerical simulations by reformulating the equations in terms of the tensor's symmetric square root.

Contribution

It presents a novel symmetric factorization of the conformation tensor that simplifies the equations of motion and enhances numerical stability in viscoelastic fluid simulations.

Findings

Improved numerical stability and accuracy in simulations.

Formulation in a Hilbert space with a well-defined energy functional.

Practical implementation benefits for Oldroyd-B and FENE-P models.

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.