Goal-oriented model adaptivity for viscous incompressible flows

Type
Article

Authors
van Opstal, T. M.
Bauman, P. T.
Prudhomme, S.
van Brummelen, E. H.

Online Publication Date
2015-04-04

Print Publication Date
2015-06

Date
2015-04-04

Abstract
© 2015, Springer-Verlag Berlin Heidelberg. 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.

Citation
Van Opstal TM, Bauman PT, Prudhomme S, van Brummelen EH (2015) Goal-oriented model adaptivity for viscous incompressible flows. Comput Mech 55: 1181–1190. Available: http://dx.doi.org/10.1007/s00466-015-1146-1.

Acknowledgements
The meshes presented in this manuscript were generated with Gmsh [12] and implementation was based on the nutils.org framework. This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO) and partly funded by the Ministry of Economic Affairs, Agriculture and Innovation (Project number 10476). Paul T. Bauman was supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. Serge Prudhomme is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He is also a participant of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.

Publisher
Springer Nature

Journal
Computational Mechanics

DOI
10.1007/s00466-015-1146-1

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