Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Cao, Shunxiang; Main, Alex; Wang, Kevin G.

doi:10.1002/nme.5817

Cited by 7 publications

(25 citation statements)

References 40 publications

(72 reference statements)

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“…Remark: A simpler version of this problem, in which the beam has uniform density and is a constant, has been solved both numerically and analytically (e.g., [33,23]). Cao et al [23] have derived the value of that optimizes the trade-off between numerical stability and accuracy, i.e.…”

Section: Model Setupmentioning

confidence: 99%

“…To circumvent this difficulty, we apply the method of manufactured solutions (e.g., [34]). Specifically, we "manufacture" the following closed-form solutions based on a simpler version of the problem with a uniform beam, which can be solved analytically [23].…”

Section: A Theoretical Study On the Effect Ofmentioning

confidence: 99%

“…Over the past decade, several research teams have investigated the use of a Robin interface condition to mitigate the numerical added mass effect [18,19,5,20,21,22,23,24,25,26,27,28,29,30]. The basic idea is to substitute the kinematic interface condition by its linear combination with the dynamic interface condition.…”

Section: Introductionmentioning

confidence: 99%

“…Nobile et al [19,5,20] and Fernandez et al [21,22] have introduced the Robin interface condition to different types of partitioned procedures and fluid/structural governing equations, and demonstrated their performance in the context of blood flow -vessel wall interaction. To solve FSI problems involving complex geometry and large deformation, Cao et al [23] have developed an algorithm to enforce the Robin interface condition using an embedded boundary method. We have also shown that when choosing the value of , there is a trade-off: smaller values of tend to improve numerical stability, while larger values give smaller numerical errors.…”

Section: Introductionmentioning

confidence: 99%

“…Examples include uniform beams and thin-walled tubes with constant thickness, density and elastic moduli. Several authors have suggested that in order to mitigate the numerical added mass effect, the value of Robin combination factor must be determined based on the material and geometry of the specific problem being solved (e.g., [18,26,23]). However, previous discussions have been focused on designing and applying a constant for the entire fluid-structure interface.…”

Section: Introductionmentioning

confidence: 99%

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A spatially varying robin interface condition for fluid‐structure coupled simulations

Cao

Wang

2020

Numerical Meth Engineering

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We present a spatially varying Robin interface condition for solving fluid-structure interaction problems involving incompressible fluid flows and non-uniform flexible structures. Recent studies have shown that for uniform structures with constant material and geometric properties, a constant one-parameter Robin interface condition can improve the stability and accuracy of partitioned numerical solution procedures.In this work, we generalize the parameter to a spatially varying function that depends on the structure's local material and geometric properties, without varying the exact solution of the coupled fluid-structure system. We present an algorithm to implement the Robin interface condition in an embedded boundary method for coupling a projection-based incompressible viscous flow solver with a nonlinear finite element structural solver. We demonstrate the numerical effects of the spatially varying Robin interface condition using two example problems: a simplified model problem featuring a non-uniform Euler-Bernoulli beam interacting with an inviscid flow, and a generalized Turek-Hron problem featuring a non-uniform, highly flexible beam interacting with a viscous laminar flow. Both cases show that a spatially varying Robin interface condition can clearly improve numerical accuracy (by up to 2 orders of magnitude in one instance) for the same computational cost. Using the second example problem, we also demonstrate and compare two models for determining the local value of the combination function in the Robin interface condition.

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Section: Model Setupmentioning

confidence: 99%

Section: A Theoretical Study On the Effect Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A spatially varying robin interface condition for fluid‐structure coupled simulations

Cao

Wang

2020

Numerical Meth Engineering

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A Robin‐Neumann scheme with quasi‐Newton acceleration for partitioned fluid‐structure interaction

Spenke

Make

Hosters

2022

Numerical Meth Engineering

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The Dirichlet-Neumann scheme is the most common partitioned algorithm for fluid-structure interaction (FSI) and offers high flexibility concerning the solvers employed for the two subproblems. Nevertheless, it is not without shortcomings: to begin with, the inherent added-mass effect often destabilizes the numerical solution severely. Moreover, the Dirichlet-Neumann scheme cannot be applied to FSI problems in which an incompressible fluid is fully enclosed by Dirichlet boundaries, as it is incapable of satisfying the volume constraint.In the last decade, interface quasi-Newton methods have proven to control the added-mass effect and substantially speed up convergence by adding a Newton-like update step to the Dirichlet-Neumann coupling. They are, however, without effect on the incompressibility dilemma. As an alternative, the Robin-Neumann scheme generalizes the fluid's boundary condition to a Robin condition by including the Cauchy stresses. While this modification in fact successfully tackles both drawbacks of the Dirichlet-Neumann approach, the price to be paid is a strong dependency on the Robin weighting parameter, with very limited a priori knowledge about good choices. This work proposes a strategy to merge these two ideas and benefit from their combined strengths. The resulting quasi-Newton-accelerated Robin-Neumann scheme is compared to both Robinand Dirichlet-Neumann variants. The numerical tests demonstrate that it does not only provide faster convergence, but also massively reduces the influence of the Robin parameter, mitigating the main drawback of the Robin-Neumann algorithm. K E Y W O R D Sinterface quasi-newton methods, partitioned fluid-structure interaction, Robin-Neumann scheme

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Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method

Chouly

Klein

2021

Numer Algor

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Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Cited by 7 publications

References 40 publications

A spatially varying robin interface condition for fluid‐structure coupled simulations

A spatially varying robin interface condition for fluid‐structure coupled simulations

A Robin‐Neumann scheme with quasi‐Newton acceleration for partitioned fluid‐structure interaction

Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method

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