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Immersed boundary simulations of flows driven by moving thin membranes

Immersed boundary simulations of flows driven by moving thin membranes
Immersed boundary simulations of flows driven by moving thin membranes

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.

Cartesian grid, Direct-forcing, Immersed boundary method, Membrane, Shell
0021-9991
Lauber, Marin
c8fa4bb5-81ad-4ccc-b24d-17dcc2d229af
Weymouth, Gabriel
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec
Lauber, Marin
c8fa4bb5-81ad-4ccc-b24d-17dcc2d229af
Weymouth, Gabriel
b0c85fda-dfed-44da-8cc4-9e0cc88e2ca0
Limbert, Georges
a1b88cb4-c5d9-4c6e-b6c9-7f4c4aa1c2ec

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

Identifiers

Local EPrints ID: 452854
URI: http://eprints.soton.ac.uk/id/eprint/452854
ISSN: 0021-9991
PURE UUID: b2c9ca51-6d27-45ed-9bc0-d2b85c53108a
ORCID for Marin Lauber: ORCID iD orcid.org/0000-0003-2191-9318
ORCID for Gabriel Weymouth: ORCID iD orcid.org/0000-0001-5080-5016

Catalogue record

Date deposited: 21 Dec 2021 17:56
Last modified: 06 Jun 2024 04:06

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Contributors

Author: Marin Lauber ORCID iD
Author: Georges Limbert

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