Numerical simulation of viscoelastic fluid–structure interaction benchmarks and their application to the human eye

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 elemen...

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Veröffentlicht in:SN applied sciences Jg. 4; H. 11; S. 1 - 16
Hauptverfasser: Drobny, Alexander, Friedmann, Elfriede
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.11.2022
Springer
Schlagworte:
Adaptive methods
Applied and Technical Physics
Chemistry/Food Science
Earth Sciences
Engineering
Environment
Finite element
Fluid–solid interactions
Materials Science
Pathology and pathophysiology of the human eye
Research Article
Viscoelastic fluids
Adaptive methods
Fluid–solid interactions
Viscoelastic fluids
Finite element
Pathology and pathophysiology of the human eye
ISSN:2523-3963, 2523-3971
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Zusammenfassung: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. Article highlights We obtain reliable results for the temporal and spatial discretization for a challenging viscoelastic FSI benchmark. We show good performance for the dual-weighted residual method for pure viscoelastic problems and for viscoelastic FSI. The viscoelasticity has a significant impact on the functionals of interest for the benchmarks and for the human eye.
ISSN:2523-3963
2523-3971
DOI:10.1007/s42452-022-05185-8