Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow

Turek, Stefan; Hron, J.

doi:10.1007/3-540-34596-5_15

Cited by 365 publications

(598 citation statements)

References 6 publications

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“…We seek to validate and evaluate the accuracy and performance of the proposed Newtonmultigrid solver for a set of FSI benchmark configurations that can be found in the literature (see [3,7,23]). …”

Section: Numerical Resultsmentioning

confidence: 99%

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Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Aulisa¹,

Bnà²,

Bornia³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper we investigate the numerical performance of a monolithic Newtonmultigrid solver with domain decomposition smoothers for the solution of a class of stationary incompressible FSI problems. The physics of the problem is described using a monolithic approach, where mass continuity and stress balance are automatically satisfied across the fluidsolid interface. The deformation of the fluid domain is taken into account within the nonlinear Newton iterations according to an Arbitrary Lagrangian Eulerian (ALE) scheme. Due to the complexity and variety of the operators, the implementation of the Jacobian matrix in the nonlinear iterations is not a trivial task. To this purpose, we make use of automatic differentiation tools for an exact computation of the Jacobian matrix. The numerical solution of steady-state problems is particularly challenging, due to the ill-conditioning of the induced stiffness matrix. Moreover, the enforcement of the incompressibility condition calls for the use of incompressible solvers either of mixed or segregated type. At each nonlinear outer iteration the resulting linearized system is solved with a geometric multigrid solver. We consider a GMRES smoother preconditioned by an Additive Schwarz Method (ASM). The domain decomposition of the preconditioner is driven by the natural splitting between fluid and solid domain. The numerical results of some benchmark tests for steady-state cases show agreement with the literature and an increased robustness with our choice of smoothers with respect to standard ones.

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Section: Numerical Resultsmentioning

confidence: 99%

“…In [20] the authors proposed a benchmark for testing and comparing different numerical methods and code implementations for fluid-structure interaction problems. This benchmark is based on the older successful flow around cylinder setting developed in [21] for incompressible laminar flow.…”

Section: Steady-state Two-dimensional Hron-turek Fsi1 Testmentioning

confidence: 99%

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Aulisa¹,

Bnà²,

Bornia³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…We have adapted the benchmark from [4]. Originally, the structure was placed horizontally, parallel to the flow, but the displacements in this case are very small.…”

Section: Test 2 Flexible Appendix In a Flowmentioning

confidence: 99%

Embedding Domain Technique for a Fluid-Structure Interaction Problem

Murea

Halanay

2013

IFIP Advances in Information and Communication Technology

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Abstract. We present a weak formulation for a steady fluid-structure interaction problem using an embedding domain technique with penalization. Except of the penalizing term, the coefficients of the fluid problem are constant and independent of the deformation of the structure, which represents an advantage of this approach. A second advantage of this model is the fact that the continuity of the stress at the fluid-structure interface does not appear explicitly. Numerical results are presented.Keywords: fluid-structure interaction, embedding domain. A Steady Fluid-Structure Interaction ProblemThe present paper is devoted to the study of the numerical behavior of an elastic structure immersed in a viscous incompressible fluid. We use Stokes equation to model the flow motion. The displacement of the structure under the flow motion will be modeled by linear elasticity equations, under the small deformations assumption. In this paper, we study the steady case.Let D ⊂ R 2 be a bounded open domain with boundary ∂D. Let Ω S 0 be the undeformed structure domain, and suppose that its boundary admits the decomposition ∂Ω S 0 = Γ D ∪ Γ 0 , where Γ 0 is a relatively open subset of the boundary. On Γ D we impose zero displacement for the structure. We assume that Ω S 0 ⊂ D. Suppose that the structure is elastic and denote by u = (u 1 , u 2 ) : Ω S 0 → R 2 its displacement. A particle of the structure with initial position at the point X will occupy the position x = ϕ (X) = X + u (X) in the deformed domainWe set Γ u = ϕ (Γ 0 ) and we suppose that Γ u does not touch the container wall, i.e. ∂D ∩ Γ u = ∅. We recall that Γ 0 is a relatively open subset. The boundary Γ u represents the moving fluid-structure interface. The boundary of the deformed D.

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“…In many cases, the mesh can adapt to the shape of the domain by using Lagrangian formulations [17] which take into account large displacements and geometric non-linearities, or Arbitrary Lagrangian-Eulerian (ALE) formulations [38]. In most solid dynamics problems and even in fluid-structure interaction problems where the solid body is subject to large deformations but still has an anchor point [62], the simulation can be approached using these methods. In other cases, however, domain displace-ments and deformations are so large that it is impossible for the mesh to adapt its shape to the new configuration without suffering from element distortion or element folding.…”

Section: Introductionmentioning

confidence: 99%

An adaptive Fixed-Mesh ALE method for free surface flows

Baiges

Codina

Pont

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian-Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.

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Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow

Cited by 365 publications

References 6 publications

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Embedding Domain Technique for a Fluid-Structure Interaction Problem

An adaptive Fixed-Mesh ALE method for free surface flows

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