Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics

Turek, Stefan; Hron, J.; Mádlík, Martin; Razzaq, Mudassar; Wobker, Hilmar; Acker, J. F.

doi:10.1007/978-3-642-14206-2_8

Cited by 48 publications

(52 citation statements)

References 29 publications

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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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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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“…From (27) and (28), the coefficients of the permeability ↵ and the drag factor C 2 can consequently be obtained as…”

Section: Intracranial Stents As Porous Mediamentioning

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%

“…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%

See 1 more Smart Citation

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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“…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%

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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Numerical Simulation and Benchmarking of a Monolithic Multigrid Solver for Fluid-Structure Interaction Problems with Application to Hemodynamics

Cited by 48 publications

References 29 publications

Modeling and simulations for fluid and rotating structure interactions

Modeling and simulations for fluid and rotating structure interactions

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

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

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