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A comparative analysis of Lagrange multiplier and penalty approaches for modelling fluid-structure interaction

Jacobus D. Brandsen (Wind Energy Group, and Aerospace Structures and Computational Mechanics Group, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands)
Axelle Viré (Wind Energy Group, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands)
Sergio R. Turteltaub (Aerospace Structures and Computational Mechanics Group, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands)
Gerard J.W. Van Bussel (Wind Energy Group, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands)

Engineering Computations

ISSN: 0264-4401

Article publication date: 21 September 2020

Issue publication date: 17 June 2021

144

Abstract

Purpose

When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis.

Design/methodology/approach

In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder.

Findings

The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori.

Originality/value

Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

Keywords

Acknowledgements

This work was supported by the Rijksdienst voor Ondernemend Nederland (RVO) under the TSE Hernieuwbare Energie funding scheme (ABIBA project).

Citation

Brandsen, J.D., Viré, A., Turteltaub, S.R. and Van Bussel, G.J.W. (2021), "A comparative analysis of Lagrange multiplier and penalty approaches for modelling fluid-structure interaction", Engineering Computations, Vol. 38 No. 4, pp. 1677-1705. https://doi.org/10.1108/EC-04-2020-0183

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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