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The Finite Element Immersed Boundary Method for the Numerical Simulation of the Motion of Red Blood Cells in Microfluidic Flows

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Book cover Numerical Methods for Differential Equations, Optimization, and Technological Problems

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 27))

Abstract

We study the mathematical modeling and numerical simulation of the motion of red blood cells (RBCs) subject to an external incompressible flow in a microchannel. RBCs are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We study two versions of the Finite Element Immersed Boundary Method (FE-IB), a semi-explicit scheme that requires a CFL-type stability condition and a fully implicit scheme that is unconditionally stable and numerically realized by a predictor-corrector continuation strategy featuring an adaptive choice of the time step sizes. The performance of the two schemes is illustrated by numerical simulations for various scenarios including the tank treading motion in microchannels and the motion through thin capillaries.

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Acknowledgements

Both authors acknowledge support by the German National Science Foundation DFG within the DFG Priority Program SPP 1253 ‘Optimierung mit partiellen Differentialgleichungen’. The first author has been further supported by the NSF grants DMS-0707602, DMS-0914788, by the BMBF within the projects ‘FROPT’ and ‘MeFreSim’, and by the ESF within the Networking Programme ‘OPTPDE’.

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Authors and Affiliations

  1. Institute of Mathematics, Universität Augsburg, 86159, Augsburg, Germany

    Ronald H. W. Hoppe & Christopher Linsenmann

  2. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA

    Ronald H. W. Hoppe

Authors
  1. Ronald H. W. Hoppe
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  2. Christopher Linsenmann
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Corresponding author

Correspondence to Ronald H. W. Hoppe .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Sergey Repin

  2. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Timo Tiihonen

  3. Mathematical Information Technology, University of Jyväskylä, Mattilanniemi 2, Jyväskylä, 40100, Finland

    Tero Tuovinen

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Hoppe, R.H.W., Linsenmann, C. (2013). The Finite Element Immersed Boundary Method for the Numerical Simulation of the Motion of Red Blood Cells in Microfluidic Flows. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_1

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  • DOI: https://doi.org/10.1007/978-94-007-5288-7_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5287-0

  • Online ISBN: 978-94-007-5288-7

  • eBook Packages: EngineeringEngineering (R0)

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