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01.06.2015 | Original Paper

# Goal-oriented model adaptivity for viscous incompressible flows

verfasst von: T. M. van Opstal, P. T. Bauman, S. Prudhomme, E. H. van Brummelen

Erschienen in: Computational Mechanics | Ausgabe 6/2015

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## Abstract

In van Opstal et al. (Comput Mech 50:779–788, 2012) airbag inflation simulations were performed where the flow was approximated by Stokes flow. Inside the intricately folded initial geometry the Stokes assumption is argued to hold. This linearity assumption leads to a boundary-integral representation, the key to bypassing mesh generation and remeshing. It therefore enables very large displacements with near-contact. However, such a coarse assumption cannot hold throughout the domain, where it breaks down one needs to revert to the original model. The present work formalizes this idea. A model adaptive approach is proposed, in which the coarse model (a Stokes boundary-integral equation) is locally replaced by the original high-fidelity model (Navier–Stokes) based on a-posteriori estimates of the error in a quantity of interest. This adaptive modeling framework aims at taking away the burden and heuristics of manually partitioning the domain while providing new insight into the physics. We elucidate how challenges pertaining to model disparity can be addressed. Essentially, the solution in the interior of the coarse model domain is reconstructed as a post-processing step. We furthermore present a two-dimensional numerical experiments to show that the error estimator is reliable.
Fußnoten
1
This is similar to a residual evaluation at a function with support on (part of) $${\partial \varOmega }_D$$, see also [27].

2
Except possibly locally if one chooses to define the test function $$({\varvec{v}},q)$$ using a mesh.

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Titel
Goal-oriented model adaptivity for viscous incompressible flows
verfasst von
T. M. van Opstal
P. T. Bauman
S. Prudhomme
E. H. van Brummelen
Publikationsdatum
01.06.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 6/2015
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-015-1146-1

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