Aufsatz
The financial support for this project is provided by the Klaus Tschira Stiftung gGmbH, Project No. 00.265.2015.
Numerical simulation of viscoelastic fluid-structure interaction engbenchmarks and their application to the human eye
Abstract
We present a numerical solution method for time-dependent viscoelastic fluid–structure interaction employing the arbitrary Lagrangian Eulerian framework. The derived monolithic variational formulation is discretized in time using the shifted Crank–Nicolson scheme and in space using the finite element method. For the linearisation we employ Newton’s method with exact Jacobians. The viscoelastic fluid is modelled either using the Oldroyd-B or a Burgers-type model. The elastic structures are non-linear hyperelastic materials. We validate the implementation on benchmark problems and numerically analyse the convergence for global mesh refinement and adaptive mesh refinement using the dual-weighted residual method. Furthermore we numerically analyse the influence of the viscoelasticity of the fluid on typical goal functionals like the drag, the lift and the displacement. The derived numerical solution method is applied to ophthalmology where we analyse the interaction of the viscoelastic vitreous with its surrounding elastic structures.
Sponsorship
Gefördert im Rahmen des Projekts DEALThe financial support for this project is provided by the Klaus Tschira Stiftung gGmbH, Project No. 00.265.2015.
Citation
@article{doi:10.17170/kobra-202303177652,
author={Drobny, Alexander and Friedmann, Elfriede},
title={Numerical simulation of viscoelastic fluid-structure interaction engbenchmarks and their application to the human eye},
journal={SN Applied Sciences},
year={2022}
}
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3000 Drobny, Alexander
3010 Friedmann, Elfriede
4000 Numerical simulation of viscoelastic fluid-structure interaction engbenchmarks and their application to the human eye / Drobny, Alexander
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5550 {{Fluid-Struktur-Wechselwirkung}}
5550 {{Viskoelastizität}}
5550 {{Finite-Elemente-Methode}}
5550 {{Adaptive Verfahren}}
7136 ##0##http://hdl.handle.net/123456789/14503
<resource xsi:schemaLocation="http://datacite.org/schema/kernel-2.2 http://schema.datacite.org/meta/kernel-2.2/metadata.xsd"> 2023-03-17T09:02:16Z 2023-03-17T09:02:16Z 2022-10-11 doi:10.17170/kobra-202303177652 http://hdl.handle.net/123456789/14503 Gefördert im Rahmen des Projekts DEAL The financial support for this project is provided by the Klaus Tschira Stiftung gGmbH, Project No. 00.265.2015. eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Fluid-solid interactions Viscoelastic fluidsng Finite element Adaptive methods Pathology and pathophysiology of the human eye 500 Numerical simulation of viscoelastic fluid-structure interaction engbenchmarks and their application to the human eye Aufsatz We present a numerical solution method for time-dependent viscoelastic fluid–structure interaction employing the arbitrary Lagrangian Eulerian framework. The derived monolithic variational formulation is discretized in time using the shifted Crank–Nicolson scheme and in space using the finite element method. For the linearisation we employ Newton’s method with exact Jacobians. The viscoelastic fluid is modelled either using the Oldroyd-B or a Burgers-type model. The elastic structures are non-linear hyperelastic materials. We validate the implementation on benchmark problems and numerically analyse the convergence for global mesh refinement and adaptive mesh refinement using the dual-weighted residual method. Furthermore we numerically analyse the influence of the viscoelasticity of the fluid on typical goal functionals like the drag, the lift and the displacement. The derived numerical solution method is applied to ophthalmology where we analyse the interaction of the viscoelastic vitreous with its surrounding elastic structures. open access Drobny, Alexander Friedmann, Elfriede doi:10.1007/s42452-022-05185-8 Klaus Tschira Stiftung gGmbH, Project No. 00.265.2015 Fluid-Struktur-Wechselwirkung Viskoelastizität Finite-Elemente-Methode Adaptive Verfahren publishedVersion eissn:2523-3971 Issue 11 SN Applied Sciences Volume 4 false Article: 299 </resource>
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