Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully Eulerian coordinates

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2016
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Richter, Thomas
Wick, Thomas
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Journal of Computational Physics. Elsevier. 2016, 321, pp. 874-891. ISSN 0021-9991. eISSN 1090-2716. Available under: doi: 10.1016/j.jcp.2016.06.015
Zusammenfassung

In this work, we develop numerical schemes for mechano-chemical fluid-structure interactions with long-term effects. We investigate a model of a growing solid interacting with an incompressible fluid. A typical example for such a situation is the formation and growth of plaque in blood vessels. This application includes two particular difficulties: First, growth may lead to very large deformations, up to full clogging of the fluid domain. We derive a simplified set of equations including a fluid-structure interaction system coupled to an ODE model for plaque growth in Arbitrary Lagrangian Eulerian (ALE) coordinates and in Eulerian coordinates. The latter novel technique is capable of handling very large deformations up to contact. The second difficulty stems from the different time scales: while the dynamics of the fluid demand to resolve a scale of seconds, growth typically takes place in a range of months. We propose a temporal two-scale approach using local small-scale problems to compute an effective wall stress that will enter a long-scale problem. Our proposed techniques are substantiated with several numerical tests that include comparisons of the Eulerian and ALE approaches as well as convergence studies.

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Fachgebiet (DDC)
510 Mathematik
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Finite elements, Fluid-structure interaction, Solid growth, Fully Eulerian approach, Arbitrary Lagrangian–Eulerian approach, Temporal multi-scales
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ISO 690FREI, Stefan, Thomas RICHTER, Thomas WICK, 2016. Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully Eulerian coordinates. In: Journal of Computational Physics. Elsevier. 2016, 321, pp. 874-891. ISSN 0021-9991. eISSN 1090-2716. Available under: doi: 10.1016/j.jcp.2016.06.015
BibTex
@article{Frei2016Longt-55770,
  year={2016},
  doi={10.1016/j.jcp.2016.06.015},
  title={Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully Eulerian coordinates},
  volume={321},
  issn={0021-9991},
  journal={Journal of Computational Physics},
  pages={874--891},
  author={Frei, Stefan and Richter, Thomas and Wick, Thomas}
}
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