Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

Thekkethil, Namshad; Sharma, Atul

doi:10.1002/fld.4746

Cited by 29 publications

(12 citation statements)

References 55 publications

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“…The present code was validated with several benchmark cases by Thekkethil & Sharma (2019) and used in a series of fish-inspired biomimetic studies (Thekkethil, Sharma & Agrawal 2018Gupta et al 2021). Further validations of the code are presented in figure 2, with good agreement between the present and published results on periodic variation of the displacements of the cylinder Y c (figure 2a) and plate-tip Y p (figure 2b).…”

Section: Code Validation Grid Independence and Domain Length Independ...supporting

confidence: 54%

“…A level set function-based immersed interface method (LS-IIM), which was proposed in our recent work (Thekkethil & Sharma 2019), is used for the present two-way coupled FMSI problem. The LS-IIM involves a block-iterative partitioned approach based hybrid Lagrangian–Eulerian method (Thekkethil & Sharma 2020).…”

Section: Mathematical Numerical and Parametric Detailsmentioning

confidence: 99%

Section: Mathematical Numerical and Parametric Detailsmentioning

confidence: 99%

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Flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate

Mittal

Sharma

2022

J. Fluid Mech.

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A fluid multi-structure interaction (FMSI) study on flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate is carried out numerically at a constant $Re=100$ . The effect of a non-dimensional gap $G^{*}$ between the two structures, and reduced velocity $U_{c}^{*}$ , on the proximity-induced coupled flow physics and vibration characteristics of the system is presented. The FMSI system shows a two-state response: state 1 at larger gaps $G^{*}\geqslant 1$ , and state 2 at smaller gaps $G^{*}\leqslant 0.5$ . At larger $U_{c}^{*}$ , the plate encounters an oscillating wake flow in state 1, while it encounters onset of gap flow in state 2. Each state relates to distinct vibration characteristics of both the structures, with the cylinder showing a vortex-induced vibration response in state 1 and a galloping response in state 2. The amplitude response of the cylinder is governed by gap flow dynamics while that of the plate is governed by the cylinder–plate vortex-interaction dynamics. In addition to the constructive and destructive vortex interactions reported earlier, a partial vortex interaction is observed here. The vortex interactions in the near wake lead to distinct vortex-shedding patterns – 2S, C(2S), 2P and a novel C(2P) – in the far wake. Separate regime maps are presented for the various types of cylinder–plate vortex interactions and vortex-shedding patterns, correlated with the amplitude, frequency and phase difference of the coupled vibrations of the cylinder and plate. The vortex dynamics shows a strong correlation with the quantitative vibration parameters, indicating the strongly coupled multi-physics characteristics of the present FMSI system.

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Section: Code Validation Grid Independence and Domain Length Independ...supporting

confidence: 54%

Section: Mathematical Numerical and Parametric Detailsmentioning

confidence: 99%

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Flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate

Mittal

Sharma

2022

J. Fluid Mech.

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“…This was achieved due to the projection of jump conditions across the interface. Thekkethil and Sharma [23] developed Level-Set based IIM formulation to solve FSI problems involving flexible bodies. Boundary conditions at interface were applied by the Level Set(LS) function which was calculated based on the geometry of solid.…”

Section: Immersed Interface Methods (Iim)mentioning

confidence: 99%

An Overview of Computational Fluid Structure Interaction: Methods and Applications

Morab,

Sharma

2020

Preprint

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“…Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces [53] to impose stress jump conditions along complex interfaces and allows for the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. Previous studies using the IIM have primarily focused on interfaces with prescribed motion [53][54][55][56] or on FSI models involving thin elastic membranes [56][57][58][59][60] with simple material descriptions. Our IIM formulation enables us to evaluate exterior fluid traction along the fluid-structure interface described by the C 0 continuous surface representation.…”

Section: Introductionmentioning

confidence: 99%

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

Kolahdouz¹,

Wells²,

Rossi³

et al. 2022

Preprint

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This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. To simplify the linear solvers needed by this formulation, we use a penalty method involving two representations of the fluid-structure interface, including one that moves with the fluid and another that moves with the immersed structure. These two representations are connected by approximate Lagrange multiplier forces that impose kinematic interface conditions. This approach also enables the use of multi-rate time stepping, which allows us to take different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. We additionally demonstrate second-order convergence for the time integration of the algorithm. To assess and validate the robustness and accuracy of the new algorithm,

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Level set function–based immersed interface method and benchmark solutions for fluid flexible‐structure interaction

Cited by 29 publications

References 55 publications

Flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate

Flow-induced coupled vibrations of an elastically mounted cylinder and a detached flexible plate

An Overview of Computational Fluid Structure Interaction: Methods and Applications

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

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