Truly monolithic algebraic multigrid for fluid–structure interaction

Gee, Michael W.; Küttler, U.; Wall, Wolfgang A.

doi:10.1002/nme.3001

Cited by 184 publications

(270 citation statements)

References 54 publications

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“…where in the last equality we have exploited that q ≤ p. Then, thanks to (25) and (13), we obtain from (24) …”

Section: Proposition 1 Consider the Following Discrete Problem For Nmentioning

confidence: 92%

“…Only few works have focused on this aspect. We mention [7,25,37] among the monolithic schemes, which build the whole non-linear system, and [33] among the partitioned schemes, which consist in the successive solution of the subproblems in an iterative framework (see also [15,5,11,4,10] in the case of the linear elasticity). In this work, we focus on partitioned strategies, whose main difficulties are:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Nobile

Pozzoli

Vergara

2014

Journal of Computational Physics

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In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant.

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“…where in the last equality we have exploited that q ≤ p. Then, thanks to (25) and (13), we obtain from (24) …”

Section: Proposition 1 Consider the Following Discrete Problem For Nmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Nobile

Pozzoli

Vergara

2014

Journal of Computational Physics

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“…In the former case, the complete non-linear system arising after the space discretization is assembled and solved with a suitable preconditioned Krylov [15,86], domain-decomposition [44,50] or multigrid [13,75] methods. In the partitioned case the successive solution of the fluid and solid subproblems in an iterative framework is carried out (see, e.g., [9,11,39,46,55,105,134]).…”

Section: Numerical Discretizationmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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“…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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Truly monolithic algebraic multigrid for fluid–structure interaction

Cited by 184 publications

References 54 publications

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Modeling and simulations for fluid and rotating structure interactions

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