A comparative analysis of Lagrange multiplier and penalty approaches for modelling fluid-structure interaction
| Autor: | Gerard van Bussel, Jacobus D. Brandsen, Sergio Turteltaub, Axelle Viré |
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| Rok vydání: | 2020 |
| Předmět: |
Body force
Computer science Boundary (topology) Lagrange multiplier Context (language use) 010103 numerical & computational mathematics Simple harmonic motion 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics symbols.namesake Finite element Immersed boundary Fluid-structure interaction 0103 physical sciences Fluid–structure interaction Applied mathematics Penalty 0101 mathematics General Engineering Immersed boundary method Finite element method Computer Science Applications Computational Theory and Mathematics symbols Software |
| Zdroj: | Engineering Computations: international journal for computer-aided engineering and software, 38(4) |
| ISSN: | 0264-4401 |
| DOI: | 10.1108/ec-04-2020-0183 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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