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arXiv · 1904.09136

Numerical Analysis of Unsteady Implicitly Constituted Incompressible Fluids: Three-Field Formulation

Patrick E. Farrell·Pablo Alexei Gazca-Orozco·Endre Süli
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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 generalises 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.

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Patrick E. Farrell, Pablo Alexei Gazca-Orozco, Endre Süli. 2019-04-19. Numerical Analysis of Unsteady Implicitly Constituted Incompressible Fluids: Three-Field Formulation. https://arxiv.org/abs/1904.09136

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