A modular,operator‐splitting scheme for fluid–structure interaction problems with thick structures

We present an operator‐splitting scheme for fluid–structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier–Stokes equations for an incompressible viscous fluid are used to model the fluid. The operator‐splitting scheme, based on the Lie splitting, separates the elastodynamics structure problem from a fluid problem in which structure inertia is included to achieve unconditional stability. We prove energy estimates associated with unconditional stability of this modular scheme for the full nonlinear FSI problem defined on a moving domain, without requiring any sub‐iterations within time steps. Two numerical examples are presented, showing excellent agreement with the results of monolithic schemes. First‐order convergence in time is shown numerically. Modularity, unconditional stability without temporal sub‐iterations, and simple implementation are the features that make this operator‐splitting scheme particularly appealing for multi‐physics problems involving FSI. Copyright © 2013 John Wiley & Sons, Ltd.     

An embedded boundary framework for compressible turbulent flow and fluid–structure computations on structured and unstructured grids

The finite volume method with exact two‐phase Riemann problems (FIVER) is a two‐faceted computational method for compressible multi‐material (fluid–fluid, fluid–structure, and multi‐fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi‐phase flow problems, FIVER is a Godunov‐type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two‐phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi‐material computations on nonbody‐fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second‐order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)‐based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time‐dependent distance to the wall because it is required by many RANS‐based turbulence models. The second algorithm addresses the robust and accurate computation of the flow‐induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter‐rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A‐18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient shape optimization for fluid–structure interaction problems

An approach for the shape optimization of fluid–structure interaction (FSI) problems is presented. It is based on a partitioned solution procedure for fluid–structure interaction, a shape representation with NURBS, and sequential quadratic programming approach for optimization within a parallel environment with MPI as direct coupling tool. The optimization procedure is accelerated by employing reduced order models based on a proper orthogonal decomposition method with snapshots and Kriging. After the verification of the FSI optimization, the functionality and efficiency of the reduced order modeling as well as the corresponding optimization procedure are investigated.     

Fluid–solid interaction problems with thermal convection using the immersed element‐free Galerkin method

In this work, the immersed element‐free Galerkin method (IEFGM) is proposed for the solution of fluid–structure interaction (FSI) problems. In this technique, the FSI is represented as a volumetric force in the momentum equations. In IEFGM, a Lagrangian solid domain moves on top of an Eulerian fluid domain that spans over the entire computational region. The fluid domain is modeled using the finite element method and the solid domain is modeled using the element‐free Galerkin method. The continuity between the solid and fluid domains is satisfied by means of a local approximation, in the vicinity of the solid domain, of the velocity field and the FSI force. Such an approximation is achieved using the moving least‐squares technique. The method was applied to simulate the motion of a deformable disk moving in a viscous fluid due to the action of the gravitational force and the thermal convection of the fluid. An analysis of the main factors affecting the shape and trajectory of the solid body is presented. The method shows a distinct advantage for simulating FSI problems with highly deformable solids. Copyright © 2009 John Wiley & Sons, Ltd.     

MPS-FEM数值分析带自由面的流固耦合问题

随着计算科学的发展,研究人员为探索流固耦合问题的物理机理而提出了众多的数值方法。其中,耦合的移动粒子半隐式方法 MPS(Moving Particle Semi-Implicit method)和有限单元法FEM(Finite Element method)为流固耦合问题的数值仿真工作提供了新的途径。本文所有流场的数值模拟工作均采用课题组自主开发的无网格法求解器MLParticle-SJTU来完成。该求解器在原始的MPS法基础上,对核函数、压力梯度模型、压力泊松方程的求解和自由面判断方式等方面进行了改进。此外,在该求解器框架内,基于FEM法拓展了针对结构场进行求解的功能。首先,对MPS和FEM方法的理论模型及其耦合策略进行了介绍。然后,采用该自研MPS-FEM耦合求解器,数值模拟了溃坝流动对弹性结构的冲击及其相互作用的标准问题。通过将结构变形及自由面波型变化等结果与已发表结果进行对比,验证了该求解器在处理带自由面剧烈变化的粘性流体和柔性变形结构的耦合作用问题上的可行性。     

Active sloshing control in a smart flexible cylindrical floating roof tank

An exact three dimensional fully-coupled hydro-elastic analysis for transient liquid sloshing in a partially-filled vertically-standing flexible circular cylindrical shell container fitted with a freely floating smart piezo-sandwich thin elastic circular plate is presented. The problem formulation is based on the linear water wave theory, the classical (Kirchhoff/Sanders) thin plate and shell models, Maxwell's equations of electrodynamics, Stokes’ transformation, and eigen-function expansions in cylindrical coordinates. The control action is achieved by combined volume displacement and volume velocity feedbacks (VDF, VVF) implemented in a second order active damping (AD) compensator via two competent evolutionary heuristic optimization techniques that systematically tune the controller gain parameters while constraining the floating panel displacement and control voltage. The uncontrolled and controlled transient responses of the coupled hydro-elastic system under various external disturbances (i.e., a harmonic base excitation, a real seismic event, a severe launch vehicle liftoff event, and a distributed impulsive transverse load on the floating panel) are calculated by means of Durbin's numerical inverse Laplace transform scheme. Moreover, the free vibration characteristics of the coupled fluid/structure interaction (FSI) system are briefly studied. The superior performance of the proposed active floating roof control configuration in effective suppression of the key hydro-elastic parameters (panel displacement, and shell displacements/stresses) is demonstrated. It is also found that, in the current FSI control problem, the Multi-objective Particle Swarm Optimization (MOPSO)-based ADC outperforms the Non-dominated Sorting Genetic Algorithm (NSGA-II)-based method, in terms of convergence rate and computational effort. Limiting cases are examined and the precision of results is verified by comparisons with the existing data as well as with the results produced by a commercial finite element package.     

Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows

The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction(FSI)models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods;however, partitioned FSI models are vulnerable to numerical("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible.As a partitioned method, the loosely hybrid coupled(LHC)method, which was introduced and validated in Young et al.(Acta Mech. Sin. 28:1030–1041, 2012), has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid–structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.     

High‐order implicit Runge–Kutta time integrators for fluid‐structure interactions

This paper presents an approach to develop high‐order, temporally accurate, finite element approximations of fluid‐structure interaction (FSI) problems. The proposed numerical method uses an implicit monolithic formulation in which the same implicit Runge–Kutta (IRK) temporal integrator is used for the incompressible flow, the structural equations undergoing large displacements, and the coupling terms at the fluid‐solid interface. In this context of stiff interaction problems, the fully implicit one‐step approach presented is an original alternative to traditional multistep or explicit one‐step finite element approaches. The numerical scheme takes advantage of an arbitrary Lagrangian–Eulerian formulation of the equations designed to satisfy the geometric conservation law and to guarantee that the high‐order temporal accuracy of the IRK time integrators observed on fixed meshes is preserved on arbitrary Lagrangian–Eulerian deforming meshes. A thorough review of the literature reveals that in most previous works, high‐order time accuracy (higher than second order) is seldom achieved for FSI problems. We present thorough time‐step refinement studies for a rigid oscillating‐airfoil on deforming meshes to confirm the time accuracy on the extracted aerodynamics reactions of IRK time integrators up to fifth order. Efficiency of the proposed approach is then tested on a stiff FSI problem of flow‐induced vibrations of a flexible strip. The time‐step refinement studies indicate the following: stability of the proposed approach is always observed even with large time step and spurious oscillations on the structure are avoided without added damping. While higher order IRK schemes require more memory than classical schemes (implicit Euler), they are faster for a given level of temporal accuracy in two dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

Hybrid algorithm for modeling of fluid-structure interaction in incompressible, viscous flows

The objective of this paper is to present and to validate a new hybrid coupling (HC) algorithm for modeling of fluid-structure interaction (FSI) in incompressible, viscous flows. The HC algorithm is able to avoid numerical instability issues associated with artificial added mass effects, which are often encountered by standard loosely coupled (LC) and tightly coupled (TC) algorithms, when modeling the FSI response of flexible structures in incompressible flow. The artificial added mass effect is caused by the lag in exchange of interfacial displacements and forces between the fluid and solid solvers in partitioned algorithms. The artificial added mass effect is much more prominent for light/flexible structures moving in water, because the fluid forces are in the same order of magnitude as the solid forces, and because the speed at which numerical errors propagate in an incompressible fluid. The new HC algorithm avoids numerical instability issues associated with artificial added mass effects by embedding Theodorsen’s analytical approximation of the hydroelastic forces in the solution process to obtain better initial estimates of the displacements. Details of the new HC algorithm are presented. Numerical validation studies are shown for the forced pitching response of a steel and a plastic hydrofoil. The results show that the HC algorithm is able to converge faster, and is able to avoid numerical instability issues, compared to standard LC and TC algorithms, when modeling the transient FSI response of a plastic hydrofoil. Although the HC algorithm is only demonstrated for a NACA0009 hydrofoil subject to pure pitching motion, the method can be easily extended to model general 3-D FSI response and stability of complex, flexible structures in turbulent, incompressible, multiphase flows.     

Validation of CFD‐CSD coupling interface methodology using commercial codes

Coupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit^® and Fluent^® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS^® environment. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison between computational fluid dynamics,fluid–structure interaction and computational structural dynamics predictions of flow-induced wall mechanics in an anatomically realistic cerebral aneurysm model

Haemodynamically induced stress plays an important role in the progression and rupture of cerebral aneurysms. The current work describes computational fluid dynamics (CFD), fluid–structure interaction (FSI) and computational structural dynamics (CSD) simulations in an anatomically realistic model of a carotid artery with two saccular cerebral aneurysms in the ophthalmic region. The model was obtained from three-dimensional (3D) rotational angiographic imaging data. CFD and FSI were studied under a physiologically representative waveform of inflow. The arterial wall was assumed elastic or hyperelastic, as a 3D solid or as a shell depending on the type of modelling used. The flow was assumed to be laminar, non-Newtonian and incompressible. The CFD, FSI and CSD models were solved with the finite elements package ADINA. Predictions of velocity field and wall shear stress (WSS) on the aneurysms made using CFD and FSI were compared. The CSD model of the aneurysms using complete geometry was compared with isolated aneurysm models. Additionally, the effects of hypertensive pressure on CSD aneurysm models are also reported. The vortex structure, WSS, effective stress, strain and displacement of the aneurysm walls showed differences, depending on the type of modelling used.     

Validation of a fluid–structure interaction model for a bileaflet mechanical heart valve

A fluid-structure interaction (FSI) model for heart valve simulation is presented. In a partitioned framework, separate fluid and structure solvers are weakly coupled, which in combination with the use of artificial compressibility in the fluid solver, leads to a stable and efficient approach. An Arbitrary Lagrangian Eulerian formulation is employed in the fluid solver to permit the accurate calculation of shear stresses next to the valve boundary. The mesh quality is maintained through a combination of smoothing and local remeshing in 3D. The FSI algorithm is validated on experiments of an idealised quasi-2D mechanical heart valve, and the efficiency of the remeshing approach is demonstrated on a realistic 3D heart-valve geometry.     

A new approach for computing the steady state fluid–structure interaction response of periodic problems

A special type of fluid–structure interaction (FSI) problems are problems with periodic boundary conditions like in turbomachinery. The steady state FSI response of these problems is usually calculated with similar techniques as used for transient FSI analyses. This means that, when the fluid and structure problem are not simultaneously solved with a monolithic approach, the problem is partitioned into a fluid and structural part and that each time step coupling iterations are performed to account for strong interactions between the two sub-domains. This paper shows that a time-partitioned FSI computation can be very inefficient to compute the steady state FSI response of periodic problems. A new approach is introduced in which coupling iterations are performed on periodic level instead of per time step. The convergence behaviour can be significantly improved by implementing existing partitioned solution methods as used for time step coupling (TSC) algorithms in the time periodic coupling (TPC) framework. The new algorithm has been evaluated by comparing the convergence behaviour to TSC algorithms. It is shown that the number of fluid–structure evaluations can be considerably reduced when a TPC algorithm is applied instead of a TSC. One of the most appealing advantages of the TPC approach is that the structural problem can be solved in the frequency domain resulting in a very efficient algorithm for computing steady state FSI responses.     

Fluid–structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model

Pulsatile turbulent flow characteristics in an axisymmetric aortic aneurysm (AA) model were analyzed numerically using a simulated physiological waveform. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this work. We investigated the effects of turbulent flow characteristics on the distribution of wall stress and flow patterns in AA models. Wall stress distributions were calculated by computational solid stress (CSS) model, which ignores the effect of the blood flow, and the FSI model that takes into account flow and solid mechanics. Our results showed that peak wall stress and peak deformation were found to occur shortly after peak systolic flow in the FSI model and at the peak luminal pressure condition in the CSS model. Further, CSS model underestimated wall stress calculations when compared to the FSI model. There were also significant differences in the structure of flow fields between the flexible and rigid wall aneurysm models. Contour plots of kinetic energy dissipation and the application of the Kolmogorov microscale suggest that the conditions that result in red blood cell damage and platelet activation most likely occur in the near-wall region of AA during turbulent flow.     

Strongly coupled simulation of fluid–structure interaction in a Francis hydroturbine

This work simulates a complex fluid flow in fluid–structure interaction (FSI). The flow under consideration is governed by Navier–Stokes equations for incompressible viscous fluids and modeled with the finite volume method. Large eddy simulation is used to simulate the unsteady turbulent flow. The structure is represented by a finite element formulation. The present work introduces a strongly coupled partitioned approach that is applied to complex flow in fluid machinery. In this approach, the fluid and structure equations are solved separately using different solvers, but are implicitly coupled into one single module based on sensitivity analysis of the important displacement and stress modes. The applied modes and their responses are used to build up a reduced‐order model. The proposed model is used to predict the unsteady flow fields of a 3D complete passage, involving in stay, guide vanes, and runner blades, for a Francis hydro turbine and FSI is considered. The computational results show that a fairly good convergence solution is achieved by using the reduced‐order model that is based on only a few displacement and stress modes, which largely reduces the computational cost, compared with traditional approaches. At the same time, a comparison of the numerical results of the model with available experimental data validates the methodology and assesses its accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

FSI research in pipeline systems – A review of the literature

This paper provides a broad overview of the literature pertaining to the dynamic analysis of fluid-filled pipe systems considering fluid–structure interaction (FSI). Various types of models and simulation algorithms of different levels of sophistication are compared and their application range discussed. The effects of fluid parameters, structural properties, fluid–structure couplings and boundary conditions on the inherent and dynamic character of pipes conveying fluid are comprehensively compared and contrasted.     

Measurements of junction coupling during water hammer in piping systems

For the analysis of the effects of fluid–structure interaction (FSI) during water hammer in piping systems, a test facility has been designed and constructed. The research objective is to show on the basis of two specific examples that the necessity of considering FSI is strongly dependent on the boundary conditions of the system. Resonance experiments on movable bends in two piping system configurations focused on junction coupling were carried out. These configurations differ in the length of the hydraulic system and in the geometry of the oscillating bend. The displacement of the bend and the pressure inside the pipe were measured for various free oscillating lengths of the bend while the rest of the piping system was restrained. The results are displayed in resonance curves and frequency spectra for the different configurations. In both cases a correlation between the pressure and the displacement spectrum shows a transfer of momentum from the fluid to the structure, but only in the configuration with the long oscillating pipe section can a reaction of the fluid on the motion of the structure be identified. Frequency shifts of the pressure and a splitting of the pressure peak were observed. The time signals confirm that the effects of FSI are most significant in one system configuration which is strongly influenced by the bend geometry. Furthermore a parameter is presented which quantifies the effects of junction coupling based on the geometrical and hydraulic properties of the bend and the system.     

Modelling techniques for fluid–solid coupling dynamics of bundle tubes vibrating and colliding in fluids

Nonlinear vibrations that occur in such bundle structures caused collisions between tubes and cross flows of the surrounding fluid. This paper presents modeling techniques for simulating the FSI dynamics of bundle tubes vibrating and colliding in fluids. A typical configuration of a three-dimensional tube bundles submerged in fluid of a cylindrical container is studied. Coupling conditions of displacement, velocity and forces are considered on the fluid-structure coupling interfaces. Contacts boundary between tubes and topological domain changes of the fluid are also considered on the fluid-structure coupling interface. Modeling techniques and algorithm are then established for flow-induced vibrations of the tubes, and collisions between tubes in fluids. The examples are presented to demonstrate the effectiveness of the proposed techniques. It has confirmed that our code produces the correct physics of the FSI problem, and capable of revealing the complex nonlinear mechanism with solid-solid contacts together with fluid-solid interactions.