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

Journal article

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.

Authors: Farrell, P; Gazca-Orozco, P; Süli, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Numerical Analysis
• Volume: 58
• Issue: 1
• Pages: 757-787
• Publication date: 2020-02-20
• Acceptance date: 2019-12-17
• DOI: 10.1137/19M125738X
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: FFR