Journal title
SIAM Journal on Numerical Analysis
DOI
10.1137/19M125738X
Issue
1
Volume
58
Last updated
2024-04-21T21:02:01.57+01:00
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
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Publication type
Journal Article
Publication date
20 Feb 2020