View/ Open
Date
2021-01-25Subject
510 Mathematics Fluid-Struktur-WechselwirkungAugeGlaskörperBurgers-GleichungNavier-Stokes-GleichungFinite-Elemente-MethodeNumerische StrömungssimulationVascular endothelial Growth FactorMetadata
Show full item record
Aufsatz
Numerical Simulation of Viscoelastic Fluid‐Structure Interaction Problems and Drug Therapy in the Eye
Abstract
The vitreous is a fluid‐like viscoelastic transparent medium located in the center of the human eye and is surrounded by hyperelastic structures like the sclera, lens and iris. This naturally gives rise to a fluid‐structure interaction (FSI) problem. While the healthy vitreous is viscoelastic and described by a viscoelastic Burgers‐type equation, the aging vitreous liquefies and is therefore modeled by the Navier‐Stokes equations. We derive a monolithic variational formulation employing the arbitrary Lagrangian Eulerian framework which is solved using the finite element method. To allow large 3D simulations the implementation is parallelized. Furthermore we study the vascular endothelial growth factor (VEGF) therapy in the vitreous which is modeled by four coupled convection‐diffusion‐reaction equations with an additional coupling to the underlying flow.
Citation
In: Proceedings in applied mathematics and mechanics (PAMM) Volume 20 / Issue 1 (2021-01-25) EISSN 1617-7061Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202101283081,
author={Drobny, Alexander and Friedmann, Elfriede},
title={Numerical Simulation of Viscoelastic Fluid‐Structure Interaction Problems and Drug Therapy in the Eye},
journal={Proceedings in applied mathematics and mechanics (PAMM)},
year={2021}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2021$n2021 1500 1/eng 2050 ##0##http://hdl.handle.net/123456789/12493 3000 Drobny, Alexander 3010 Friedmann, Elfriede 4000 Numerical Simulation of Viscoelastic Fluid‐Structure Interaction Problems and Drug Therapy in the Eye / Drobny, Alexander 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/12493=x R 4204 \$dAufsatz 4170 5550 {{Fluid-Struktur-Wechselwirkung}} 5550 {{Auge}} 5550 {{Glaskörper}} 5550 {{Burgers-Gleichung}} 5550 {{Navier-Stokes-Gleichung}} 5550 {{Finite-Elemente-Methode}} 5550 {{Numerische Strömungssimulation}} 5550 {{Vascular endothelial Growth Factor}} 7136 ##0##http://hdl.handle.net/123456789/12493
2021-02-10T16:10:15Z 2021-02-10T16:10:15Z 2021-01-25 doi:10.17170/kobra-202101283081 http://hdl.handle.net/123456789/12493 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ 510 Numerical Simulation of Viscoelastic Fluid‐Structure Interaction Problems and Drug Therapy in the Eye Aufsatz The vitreous is a fluid‐like viscoelastic transparent medium located in the center of the human eye and is surrounded by hyperelastic structures like the sclera, lens and iris. This naturally gives rise to a fluid‐structure interaction (FSI) problem. While the healthy vitreous is viscoelastic and described by a viscoelastic Burgers‐type equation, the aging vitreous liquefies and is therefore modeled by the Navier‐Stokes equations. We derive a monolithic variational formulation employing the arbitrary Lagrangian Eulerian framework which is solved using the finite element method. To allow large 3D simulations the implementation is parallelized. Furthermore we study the vascular endothelial growth factor (VEGF) therapy in the vitreous which is modeled by four coupled convection‐diffusion‐reaction equations with an additional coupling to the underlying flow. open access Drobny, Alexander Friedmann, Elfriede doi:10.1002/pamm.202000260 Fluid-Struktur-Wechselwirkung Auge Glaskörper Burgers-Gleichung Navier-Stokes-Gleichung Finite-Elemente-Methode Numerische Strömungssimulation Vascular endothelial Growth Factor publishedVersion EISSN 1617-7061 Issue 1 Proceedings in applied mathematics and mechanics (PAMM) Volume 20 false e202000260
The following license files are associated with this item: