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On the use of the notion of suitable weak solutions in CFD
Author(s) -
Guermond JeanLuc
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1853
Subject(s) - finite element method , mathematics , computational fluid dynamics , navier–stokes equations , regularization (linguistics) , compressibility , a priori and a posteriori , discontinuous galerkin method , commutator , large eddy simulation , weak formulation , mathematical analysis , algebra over a field , computer science , pure mathematics , turbulence , boundary value problem , engineering , mechanics , physics , artificial intelligence , philosophy , lie conformal algebra , structural engineering , epistemology
The notion of suitable weak solutions for the three‐dimensional incompressible Navier–Stokes equations together with some standard regularization techniques for constructing these solutions is reviewed. The novel result presented in this paper is that Faedo–Galerkin weak solutions to the Navier–Stokes equations are suitable provided they are constructed using finite‐dimensional spaces having a discrete commutator property and satisfying a proper inf–sup condition. Low‐order mixed finite element spaces appear to be acceptable for this purpose. Connections between the notion of suitable solutions and LES modeling are investigated. A proposal for a large eddy scale model based on the notion of suitable solutions is made and numerically illustrated. Copyright © 2008 John Wiley & Sons, Ltd.