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Reference map technique for incompressible fluid–structure interaction

Published online by Cambridge University Press:  30 June 2020

Chris H. Rycroft*
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02139, USA Mathematics Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
Chen-Hung Wu
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02139, USA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Yue Yu
Department of Mathematics, Lehigh University, Bethlehem, PA 18015, USA
Ken Kamrin*
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Email addresses for correspondence:,
Email addresses for correspondence:,


We present a general simulation approach for fluid–solid interactions based on the fully Eulerian reference map technique. The approach permits the modelling of one or more finitely deformable continuum solid bodies interacting with a fluid and with each other. A key advantage of this approach is its ease of use, as the solid and fluid are discretized on the same fixed grid, which greatly simplifies the coupling between the phases. We use the method to study a number of illustrative examples involving an incompressible Navier–Stokes fluid interacting with multiple neo-Hookean solids. Our method has several useful features including the ability to model solids with sharp corners and the ability to model actuated solids. The latter permits the simulation of active media such as swimmers, which we demonstrate. The method is validated favourably in the flag-flapping geometry, for which a number of experimental, numerical and analytical studies have been performed. We extend the flapping analysis beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping.

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© The Author(s), 2020. Published by Cambridge University Press

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