NKS for Fully Coupled Fluid-Structure Interaction with Application

Barker, Andrew T.; Cai, Xiao‐Chuan

doi:10.1007/978-3-642-02677-5_30

Cited by 6 publications

(11 citation statements)

References 11 publications

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“…In this case an important role is played by the preconditioner used to solve the linear system that is obtained after discretization and linearization of the problem. Among the different choices described in literature, the domain decomposition preconditioners like the additive Schwarz preconditioner show to be effective [6].…”

Section: Modular Versus Non-modular Algorithmsmentioning

confidence: 99%

“…It is also possible to neglect the shape derivatives, in which case the Jacobian matrix is inherited by the computation of the residual in (3.1), we call J QN the matrix resulting from the approximated Jacobian; this is simpler to implement and computationally less expensive, although in some circumstances it fails to converge [18] or the convergence rate is very low [23]. In [6] this method has been adopted, while in [22] a linear fluid model on a fixed domain is used to compute an approximation of the Jacobian matrix, leading to a very cheap Jacobian and "large" number of quasi-Newton iterations.…”

Section: Nonlinearitiesmentioning

confidence: 99%

“…The fully coupled nonlinear problem can be discretized in time by considering all the terms in the equations implicitly, that leads to a fully implicit method [7,37,24,27,6,15]. This is the most stable but also most expensive choice.…”

mentioning

confidence: 99%

“…Otherwise the time discretized problem can be linearized via Newton's method, either exact, as in [7,24,18,37,27], or inexact, as in [6,21,12,23,13]. In the Newton/quasi-Newton approaches the Jacobian matrix is often available only as matrix-vector multiplication (it is the case in [18]).…”

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confidence: 99%

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Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Crosetto¹,

Deparis²,

Fourestey³

et al. 2011

SIAM J. Sci. Comput.

111

157

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Abstract. The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In Fluid-Structure Interaction (FSI, in short) for haemodynamic applications, parallelization and scalability are key issues (see [20]). In this work we introduce a class of parallel preconditioners for the FSI problem obtained by exploiting the block-structure of the linear system. We stress the possibility of extending the approach to a general linear system with a block-structure, then we provide a bound in the condition number of the preconditioned system in terms of the conditioning of the preconditioned diagonal blocks, finally we show that the construction and evaluation of the devised preconditioner is modular. The preconditioners are tested on a benchmark 3D geometry discretized in both a coarse and a fine mesh, as well as on two physiological aorta geometries. The simulations that we have performed show an advantage in using the block preconditioners introduced and confirm our theoretical results.Key words. Blood-Flow Models , Fluid-Structure Interaction , Finite Elements , Preconditioners , Parallel Algorithms AMS subject classifications. 65M60 , 65F08 , 65Y05 , 76Z051. Introduction . The modeling of the cardiovascular system is receiving increasing attention from both the medical and mathematical environments because of, from the one hand, the great influence of haemodynamics on cardiovascular diseases ([20] chap 1), and, from the other hand, its challenging complexity that keeps open the debate about the setting up of appropriate models and algorithms. A wide variety of approaches can be found in literature, dealing with different formulations of the problem and solution strategies.In this introduction we refrain from describing the models that can be used to simulate the physiological behavior of the arterial vessels; for that we address the interested reader to [20]. We give instead an overview of some of the most popular methodologies to solve numerically the coupled system of equations arising from the haemodynamic model: those that describe the flowfield variables (blood velocity and pressure) and those that govern the mechanical deformation of the vessel walls (the "structure"). The first distinction comes from the formulation of the problem.A common choice in the FSI context is to describe the fluid equations using an Arbitrary Lagrangian-Eulerian frame of reference (see e.g. [31]). The advantage with respect to an Eulerian description is that the coupling can be satisfied exactly on the fluid-structure interface. However the introduction of a new equation for the fluid domain motion is required, and its dependence on the solution of the FSI problem introduces a further nonlinearity.A different approach consists of a space-time formulation which adopts the Eulerian framework. Usually, the latter involves a discretization of the computational domain in time slab...

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Section: Modular Versus Non-modular Algorithmsmentioning

confidence: 99%

Section: Nonlinearitiesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Crosetto¹,

Deparis²,

Fourestey³

et al. 2011

SIAM J. Sci. Comput.

111

157

View full text Add to dashboard Cite

show abstract

“…We refer to [24,1,2,22,46,16,3,4,5,48,49] for details. In particular, when stable mixed finite element pairs are used, we can develop robust block preconditioners based on the well-posedness shown in Theorem 1.…”

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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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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A Domain Decomposition Based Parallel Inexact Newton’s Method with Subspace Correction for Incompressible Navier-Stokes Equations

Cai

2009

Lecture Notes in Computer Science

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There are two major types of approaches for solving the incompressible Navier-Stokes equations. One of them is the so-called projection method, in which the velocity field and the pressure field are solved separately. This method is very efficient, but is difficult to be extended to another multi-physics problem when an appropriate splitting is not available. The other approach is the fully coupled method in which the velocity and pressure fields stay together throughout the computation. The coupled approach can be easily extended to other multiphysics problems, but it requires the solution of some rather difficult linear and nonlinear algebraic systems of equations. The paper focuses on a fully coupled domain decomposition based parallel inexact Newton's method with subspace correction for incompressible Navier-Stokes equations at high Reynolds numbers. The discussion is restricted to the velocity-vorticity formulation of the Navier-Stokes equations, but the idea can be generalized to other multi-physics problems.

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NKS for Fully Coupled Fluid-Structure Interaction with Application

Cited by 6 publications

References 11 publications

Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Modeling and simulations for fluid and rotating structure interactions

A Domain Decomposition Based Parallel Inexact Newton’s Method with Subspace Correction for Incompressible Navier-Stokes Equations

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