Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation

Author: 

Farrell, P
Gazca-Orozco, P
Süli, E

Publication Date: 

20 February 2020

Journal: 

SIAM Journal on Numerical Analysis

Last Updated: 

2020-07-23T22:03:30.75+01:00

Issue: 

1

Volume: 

58

DOI: 

10.1137/19M125738X

page: 

757-787

abstract: 

In the classical theory of fluid mechanics a linear relationship between the shear stress and the symmetric velocity gradient tensor is often assumed. Even when a nonlinear relationship is assumed, it is typically formulated in terms of an explicit relation. Implicit constitutive models provide a theoretical framework that generalizes this, allowing for general implicit constitutive relations. Since it is generally not possible to solve explicitly for the shear stress in the constitutive relation, a natural approach is to include the shear stress as a fundamental unknown in the formulation of the problem. In this work we present a mixed formulation with this feature, discuss its solvability and approximation using mixed finite element methods, and explore the convergence of the numerical approximations to a weak solution of the model.

Symplectic id: 

995456

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article