Computational Mechanics

, Volume 55, Issue 6, pp 1181–1190 | Cite as

Goal-oriented model adaptivity for viscous incompressible flows

  • T. M. van Opstal
  • P. T. Bauman
  • S. Prudhomme
  • E. H. van Brummelen
Original Paper

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.

Keywords

Finite element Boundary element Adaptivity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • T. M. van Opstal
    • 1
  • P. T. Bauman
    • 2
  • S. Prudhomme
    • 3
  • E. H. van Brummelen
    • 4
  1. 1.Department of Mathematical SciencesNorwegian University of Science and Technology (NTNU)TrondheimNorway
  2. 2.Mechanical and Aerospace Engineering, Computational and Data-Enabled Science and Engineering, University at BuffaloState University of New YorkBuffaloUSA
  3. 3.Département de Mathématiques et de Génie IndustrielÉcole Polytechnique de MontréalMontréalCanada
  4. 4.Department of Mechanical Engineering, Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenNetherlands

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