Immersed boundary simulations of flows driven by moving thin membranes

Lauber, Marin, Weymouth, Gabriel and Limbert, Georges (2022) Immersed boundary simulations of flows driven by moving thin membranes. Journal of Computational Physics, 457, [111076]. (doi:10.1016/j.jcp.2022.111076).

Record type: Article

Abstract

Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modeling flexibility compared to body-fitted grid methods. However, thin geometries, such as shells and membranes, cause a violation of the boundary conditions across the surface for many immersed boundary projection algorithms. Using a one-dimensional analytical derivation and multi-dimensional numerical simulations, this manuscript shows that adjustment of the Poisson matrix itself is require to avoid large velocity, pressure, and force prediction errors when the pressure jump across the interface is substantial and that these errors increase with Reynolds number. A new minimal thickness modification is developed for the Boundary Data Immersion Method (BDIM-σ), which avoids these issues while still enabling the use of efficient projection algorithms for high-speed immersed surface simulations.

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Journal_of_Computational_Physics D-21-00488-R1 - Accepted Manuscript

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Accepted/In Press date: 6 December 2021

e-pub ahead of print date: 15 February 2022

Published date: 15 May 2022

Additional Information: Funding Information: The authors would like to acknowledge financial support from the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling grant EP/L015382/1 , and the use of the IRIDIS High Performance Computing Facility and associated support services at the University of Southampton. The authors gratefully acknowledge Bernat Font and Artur K. Lidtke for their helpful comments on an early version of this manuscript. Finally, we would like to acknowledge the reviewers that made excellent comments and suggestions that, we believe, helped greatly improve this manuscript. Publisher Copyright: © 2022 Elsevier Inc.

Keywords: Cartesian grid, Direct-forcing, Immersed boundary method, Membrane, Shell

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