A monolithic Lagrangian approach for fluid–structure interaction problems

Ryzhakov, Pavel; Rossi, Riccardo; Idelsohn, Sergio; Oñate, Eugenio

doi:10.1007/s00466-010-0522-0

Cited by 135 publications

(136 citation statements)

References 29 publications

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“…We prove this theorem by verifying the Brezzi's conditions (40) and (41). First we verify the boundedness ofã(·, ·) and its coercivity in Z h .…”

Section: Theorem 1 Assume the Following Conditionsmentioning

confidence: 73%

“…Especially, the partitioned method turns out to be unconditionally unstable with an explicit scheme, or to be a oscillating iteration with questionable convergence when an implicit scheme is used, if the densities of fluid and structure become comparable or if the domain has a slender shape. Such phenomenon is also called the added-mass effect [39,40,32,26], which the monolithic algorithm can completely avoid.…”

Section: Algorithm 1 Ale Methods For Fsi Involving An Elastic Rotormentioning

confidence: 99%

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Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure which is suitable for the application of arbitrary LagrangianEulerian (ALE) method in FSI simulation. Additionally, a novel ALE mapping method is designed to generate the moving fluid mesh while the deformable structure spins in a non-axisymmetric fluid channel. The structure velocity is adopted as the principle unknown to form a monolithic saddle-point system together with fluid velocity and pressure. We discretize the nonlinear saddle-point system with mixed finite element method and Newton's linearization, and prove that the derived saddle-point problem is well-posed. The developed methodology is applied to a self-defined elastic structure and a realistic hydroturbine under a prescribed angular velocity. Both illustrate the satisfactory numerical results of an elastic structure that is deforming and rotating while interacting with the fluid. The numerical validation is also conducted to demonstrate the modeling consistency.

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“…We prove this theorem by verifying the Brezzi's conditions (40) and (41). First we verify the boundedness ofã(·, ·) and its coercivity in Z h .…”

Section: Theorem 1 Assume the Following Conditionsmentioning

confidence: 73%

Section: Algorithm 1 Ale Methods For Fsi Involving An Elastic Rotormentioning

confidence: 99%

Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…Note also that discrete operators follow the definitions given by Eqs. (13)- (18), but are now calculated using the current configuration X n+1 according to updated Lagrangian approach [15], [25]. The forceF int in Eq.…”

Section: Finite Element Formulation For the Liquidmentioning

confidence: 99%

“…Solve the gas problem (using real part of the Eulerian domain Ω Er ) (Eqs. (24), (25) and (26)) equipped with the interface Dirichlet boundary condition applied to the fictitious nodes. Output: velocity and pressurev n+1 andp n+1 in Ω n+1 E .…”

Section: "Switch Off" the Fictitious Eulerian Elements (ω E F )mentioning

confidence: 99%

An embedded approach for immiscible multi‐fluid problems

Ryzhakov

Jarauta

2015

Numerical Methods in Fluids

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An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated and its potential applications are shown.

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“…Unlike in the aforementioned works, our approach is however more direct: Firstly, the hp-adaptivity is implemented on top of a usual partitioned-based FSI formulation with arbitrary Lagrangian-Eulerian (ALE) description of the fluid and structure domains. It is expected that an iterative solver used is more stable since the resulting equations are smaller and generally better conditioned [6]. The partitioned approach involves separate solutions for fluid and structure domains, together with iterations for each solution to converge to a specified stopping criterion that satisfies both domains as well as the interface conditions.…”

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confidence: 99%

Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

Abas¹,

Abdul-Rahman²

2013

IJCTE

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Abstract-Recent advances in computational studies of fluid flows with structural interactions suggest that significant contributions have been made towards reliable solutions to the problem. Achieving accurate solutions however remains a considerable task since enormous amount of computer time and memory are usually needed. This applies particularly to a partitioned approach in which structure and fluid are solved separately. This paper attempts to solve fluid-structure interaction (FSI) problems with an hp-adaptive finite element method (hp-FEM). The FSI problem is formulated based on a partitioned approach and Arbitrary Lagrangian-Eulerian (ALE) descriptions for the incompressible fluid and structure domains. The hp-adaptivity is implemented with an a posteriori error estimator and adaptation to minimize error in energy norm. The automatic mesh adaptation over the triangular mesh is achieved with red-green-blue refinement technique. A strategy for mesh refinement to occur at prescribed key points is used for effective mesh adaptivity. The hp-adaptive approach is assessed with traditional uniform mesh refinement and also an h-adaptive method on a benchmark test case. From the error convergence, the hp-adaptive method is shown to be a viable approach in acquiring accurate solution of a partitioned-based FSI analysis without significant compromise in computational time and memory. It is also found that the convergence of solution in fluid and structure domains is considerably sensitive to the aspect ratios of triangular elements.Index Terms-Fluid structure interaction, finite element analysis, hp-FEM, a posteriori error estimates. I. INTRODUCTIONAnalysis of fluid flows that are being impeded by an elastic structure poses a particularly challenging task as it is a complex multiphysics problem in which fluid and structure are mutually coupled along a shared boundary. The past few years have seen growing interests in the analysis of fluid-structure interaction (FSI) problems that arise in interdisciplinary fields spanning from biomechanical to microsystems applications [1], [2]. Hence, accurate tools that provide deep understanding of the phenomenon are always of significant interests. Despite considerable advances in the computational analysis of the FSI problems, achieving reasonable accuracy of the solution without excessive computational resources remains an open challenge. This paper attempts to solve the fluid-structure interaction problem with an hp-adaptive finite element method (hp-FEM), in which a careful decision in local mesh refinement (h) combined with increase in polynomial order Manuscript received October 5, 2012; revised January 17, 2013. This work was supported in part by the Malaysia Ministry of Higher Education under its fellowships scheme.The authors are with the School of Mechanical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia (e-mail: aizat_abas@ yahoo.com; arahman@ eng.usm.my).(p) based on an error indicator is expected to result in highly accurate solution. I...

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A monolithic Lagrangian approach for fluid–structure interaction problems

Cited by 135 publications

References 29 publications

Modeling and simulations for fluid and rotating structure interactions

Modeling and simulations for fluid and rotating structure interactions

An embedded approach for immiscible multi‐fluid problems

Finite Element Method for Fluid Structure Interaction with hp-Adaptivity

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