FEM multigrid techniques for fluid–structure interaction with application to hemodynamics

Razzaq, Mudassar; Damanik, H.; Hron, J.; Ouazzi, Abderrahim; Turek, Stefan

doi:10.1016/j.apnum.2010.12.010

Cited by 33 publications

(42 citation statements)

References 20 publications

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“…In [12] a geometric multigrid solver with a Multilevel Pressure Schur Complement (MPSC) Vanka-like smoother is considered, with applications to nonstationary FSI problems in biomechanics. Applications of this scheme to hemodynamics are also addressed in [22,14]. Monolithic Newton-Krylov algorithms are studied in [8,26].…”

Section: Introductionmentioning

confidence: 99%

“…A partitioned method in which multigrid is used either within the fluid and solid solves or as an outer iteration is addressed in [16,18]. Other numerical studies are available in the literature on the use of domain decomposition Vanka-type smoothers for multigrid both in Computational Fluid Dynamics (CFD) and in Computational Solid Mechanics (CSM) [1,19,24,25,14,2].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Zhao, et al [18] have used the ALE to simulate the fluid-structure interaction of the AP1000 water tank subjected to earthquakes and obtained the optimal height of water to reduce seismic responses. It is thus clear that the ALE based fluid-structure interaction algorithm can be used to deal with the coupling of liquid and its corresponding storage vessel [19][20][21]. Thus, the ALE based fluid-structure interaction approach is adopted in this study for analyses of the water conveyance tunnel subjected to earthquakes.…”

Section: Introductionmentioning

confidence: 99%

Parallel Dynamic Analysis of a Large-Scale Water Conveyance Tunnel under Seismic Excitation Using ALE Finite-Element Method

et al. 2016

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Abstract:Parallel analyses about the dynamic responses of a large-scale water conveyance tunnel under seismic excitation are presented in this paper. A full three-dimensional numerical model considering the water-tunnel-soil coupling is established and adopted to investigate the tunnel's dynamic responses. The movement and sloshing of the internal water are simulated using the multi-material Arbitrary Lagrangian Eulerian (ALE) method. Nonlinear fluid-structure interaction (FSI) between tunnel and inner water is treated by using the penalty method. Nonlinear soil-structure interaction (SSI) between soil and tunnel is dealt with by using the surface to surface contact algorithm. To overcome computing power limitations and to deal with such a large-scale calculation, a parallel algorithm based on the modified recursive coordinate bisection (MRCB) considering the balance of SSI and FSI loads is proposed and used. The whole simulation is accomplished on Dawning 5000 A using the proposed MRCB based parallel algorithm optimized to run on supercomputers. The simulation model and the proposed approaches are validated by comparison with the added mass method. Dynamic responses of the tunnel are analyzed and the parallelism is discussed. Besides, factors affecting the dynamic responses are investigated. Better speedup and parallel efficiency show the scalability of the parallel method and the analysis results can be used to aid in the design of water conveyance tunnels.

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“…We concentrate on cerebral aneurysms, presenting numerical studies for both 2D and 3D aneurysm configurations. The 2D geometry is based on the benchmark setting proposed in [27] and [21], and the 3D shape is an extension of the 2D configuration based on a real aneurysm view proposed on [27]. We also propose simulations of stenting technology applied to the 2D and 3D geometries.…”

Section: Introductionmentioning

confidence: 99%

“…Both multigrid and domain decomposition methods draw a lot of attention within the FSI community. In [27] and [21], where hemodynamics applications are also addressed, a geometric multigrid solver with a Multilevel Pressure Schur Complement (MPSC) Vanka-like smoother is considered. In [30] a Newton-Krylov algorithm with an overlapping additive Schwarz preconditioner is considered in applications to parallel three-dimensional blood flow simulations.…”

Section: Introductionmentioning

confidence: 99%

Fluid-Structure Simulations and Benchmarking of Artery Aneurysms Under Pulsatile Blood Flow

Aulisa¹,

Bornia²,

Calandrini³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper Fluid-structure interaction (FSI) simulations of artery aneurysms are carried out where both the fluid flow and the hyperelastic material are incompressible. We focus on time-dependent formulations adopting a monolithic approach, where the deformation of the fluid domain is taken into account according to an Arbitrary Lagrangian Eulerian (ALE) scheme. The exact Jacobian matrix is implemented by using automatic differentiation tools. The system is modeled using a specific equation shuffling that assures an optimal pivoting. We propose to solve the resulting linearized system at each nonlinear outer iteration with a GMRES solver preconditioned by a geometric multigrid algorithm with an Additive Schwarz Method (ASM) smoother.In order to test our numerical method on possible hemodynamics applications, we describe several benchmark settings. The configurations consist of realistic artery aneurysms where hybrid meshes are employed. Both two and three-dimensional benchmarks are considered. We show numerical results for the described aneurysm geometries focusing on pulsatile inflow conditions. Parallel implementation is addressed and a case of endovascular stent implantation on a cerebral aneurysm is presented. 955Available online at www.eccomasproceedia.org Eccomas Proceedia COMPDYN (2017) 955-974

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FEM multigrid techniques for fluid–structure interaction with application to hemodynamics

Cited by 33 publications

References 20 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

Parallel Dynamic Analysis of a Large-Scale Water Conveyance Tunnel under Seismic Excitation Using ALE Finite-Element Method

Fluid-Structure Simulations and Benchmarking of Artery Aneurysms Under Pulsatile Blood Flow

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