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

Kolahdouz, Ebrahim M.; Bhalla, Amneet Pal Singh; Scotten, Lawrence N.; Craven, Brent A.; Griffith, Boyce E.

doi:10.1016/j.jcp.2021.110442

Cited by 18 publications

(25 citation statements)

References 127 publications

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“…Additionally, our simulations demonstrate that structures with low and near-equal density ratios are successfully modeled with reasonable time step sizes with no apparent restrictions caused by added mass instabilities. We previously reported this advantage of the method for rigid-body FSI [12]. This work provides further evidence that the ILE formulation can handle flexible-body FSI problems with large added mass effects.…”

Section: Introductionsupporting

confidence: 53%

“…The key challenge in these methods, however, is related to developing effective and accurate coupling operators and boundary conditions that link the Eulerian and Lagrangian variables; see a recent review by Griffith and Patankar [9] along with those by Peskin [8], Mittal [10], and Sotiropoulos and Yang [11]. This paper extends our earlier work to integrate partitioned and immersed approaches to FSI by generalizing our recently developed immersed Lagrangian-Eulerian formulation for fluid-rigid structure interaction [12] to problems involving flexible structures described by nonlinear elastic material models. To do so, in this work, the equations of motion for the rigid body are replaced by the equations of elastodynamics.…”

Section: Introductionmentioning

confidence: 83%

“…Methods based on distributed Lagrange multipliers (DLM) form another class of immersed formulations, and since their original development by Glowinski et al [28,29], different variations of this approach have been reported for fluid-flexible structure interaction [30][31][32][33][34]. To our knowledge, except for our earlier work on rigid-body FSI [12], all existing DLM formulations use voluemtric coupling schemes to connect the fluid and solid variables. Other immersed formulations for FSI include the moving least square direct forcing immersed boundary method [35][36][37] and fully Eulerian approaches based on finite difference [38][39][40] or finite element [41,42] techniques.…”

Section: Introductionmentioning

confidence: 99%

“…As in our earlier work [12], our goal is to create a numerical scheme with the geometrical and domain solution flexibility of the IB method and an accuracy comparable to body-fitted approaches for which sharp resolution of flows and stresses is achieved up to the fluid-structure interface. Unlike many IB methods, our ILE approach uses distinct momentum equations for the fluid and solid subregions, and it uses a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through interface conditions.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Kolahdouz¹,

Wells²,

Rossi³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus, the most important part of SIB methods is the method used to reconstruct the velocity field at the IB nodes. Recent works focus on the adaptive mesh refinement techniques to enhance the local resolution near the wall [85]. Due to the incompressibility constraint (∇ • v f = 0), the staggered grid approach [54,59,86] is typically implemented to ensure that the divergence-free condition is satisfied exactly at the cell center (pressure node).…”

Section: Finite Difference Methodsmentioning

confidence: 99%

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

Usta

Aidun

et al. 2022

Fluids

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Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.

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A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

He,

Lu,

2024

Numerical Methods in Fluids

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This article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative‐Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell‐based smoothed finite element method (CSFEM) using four‐node quadrilateral (Q4) elements for a cost‐effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak‐form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under‐integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative‐Jacobian elements. The developed technique is easy‐to‐implement and has been tested in various FSI examples adopting both fine and distorted meshes.

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

Cited by 18 publications

References 127 publications

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

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

Computational Methods for Fluid-Structure Interaction Simulation of Heart Valves in Patient-Specific Left Heart Anatomies

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

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