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Unified Continuum modeling of fluid-structure interaction
KTH, School of Computer Science and Communication (CSC). (Computational Technology Laboratory)ORCID iD: 0000-0003-4256-0463
KTH, School of Computer Science and Communication (CSC). (Computational Technology Laboratory)ORCID iD: 0000-0002-1695-8809
KTH, School of Computer Science and Communication (CSC). (Computational Technology Laboratory)
2011 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 21, no 3, 491-513 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we describe an incompressible Unified Continuum(UC) model in Euler (laboratory) coordinates with a moving mesh for tracking the fluid-structure interface as part of the discretization, allowing simple and general formulation and efficient computation. The model consists of conservation equations for mass and momentum, a phase convection equation and a Cauchy stress and phase variable theta as data for defining material properties and constitutive laws. We target realistic 3D turbulent fluid-structure interaction (FSI) applications, where we show simulation results of a flexible flag mounted in the turbulent wake behind a cube as a qualitative test of the method, and quantitative results for 2D benchmarks, leaving adaptive error control for future work. We compute piecewise linear continuous discrete solutions in space and time by a general Galerkin (G2) finite element method (FEM). We introduce and compensate for mesh motion by defining a local arbitrary Euler-Lagrange (ALE) map on each space-time slab as part of the discretization, allowing a sharp phase interface given by theta on cell facets. The Unicorn implementation is published as part of the FEniCS Free Software system for automation of computational mathematical modeling. Simulation results are given for a 2D stationary convergence test, indicating quadratic convergence of the displacement, a simple 2D Poiseuille test for verifying correct treatment of the fluid-structure interface, showing quadratic convergence to the exact drag value, an established 2D dynamic flag benchmark test, showing a good match to published reference solutions and a 3D turbulent flag test as indicated above.

Place, publisher, year, edition, pages
World Scientific, 2011. Vol. 21, no 3, 491-513 p.
Keyword [en]
Partial differential equations, numerical analysis, fluid mechanics, mechanics for deformable solids
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-32610DOI: 10.1142/S021820251100512XISI: 000288713700003Scopus ID: 2-s2.0-79952849407OAI: oai:DiVA.org:kth-32610DiVA: diva2:411758
Funder
Swedish e‐Science Research Center
Note

QC 20110419

Available from: 2011-04-19 Created: 2011-04-18 Last updated: 2017-12-11Bibliographically approved

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Hoffman, Johan

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