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Bounds on outputs of the exact weak solution of the three‐dimensional Stokes problem
Author(s) -
Cheng Zhong,
Ghomeshi Shahin,
Paraschivoiu Marius
Publication year - 2009
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.1989
Subject(s) - mathematics , stokes flow , poisson's equation , exact solutions in general relativity , work (physics) , compressibility , flow (mathematics) , flux (metallurgy) , advection , mathematical analysis , square (algebra) , incompressible flow , channel (broadcasting) , stokes number , geometry , physics , mechanics , computer science , reynolds number , computer network , materials science , turbulence , metallurgy , thermodynamics
A method for obtaining rigorous upper and lower bounds on an output of the exact weak solution of the three‐dimensional Stokes problem is described. Recently bounds for the exact outputs of interest have been obtained for both the Poisson equation and the advection‐diffusion‐reaction equation. In this work, we extend this approach to the Stokes problem where a novel formulation of the method also leads to a simpler flux calculation based on the directly equilibrated flux method. To illustrate this technique, bounds on the flowrate are calculated for an incompressible creeping flow driven by a pressure gradient in an endless square channel with an array of rectangular obstacles in the center. Copyright © 2009 John Wiley & Sons, Ltd.