A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.     

A three‐dimensional hybrid meshfree‐Cartesian scheme for fluid–body interaction

A numerical method based on a hybrid meshfree‐Cartesian grid is developed for solving three‐dimensional fluid–solid interaction (FSI) problems involving solid bodies undergoing large motion. The body is discretized and enveloped by a cloud of meshfree nodes. The motion of the body is tracked by convecting the meshfree nodes against a background of Cartesian grid points. Spatial discretization of second‐order accuracy is accomplished by the combination of a generalized finite difference (GFD) method and conventional finite difference (FD) method, which are applied to the meshfree and Cartesian nodes, respectively. Error minimization in GFD is carried out by singular value decomposition. The discretized equations are integrated in time via a second‐order fractional step projection method. A time‐implicit iterative procedure is employed to compute the new/evolving position of the immersed bodies together with the dynamically coupled solution of the flow field. The present method is applied on problems of free falling spheres and tori in quiescent flow and freely rotating spheres in simple shear flow. Good agreement with published results shows the ability of the present hybrid meshfree‐Cartesian grid scheme to achieve good accuracy. An application of the method to the self‐induced propulsion of a deforming fish‐like swimmer further demonstrates the capability and potential of the present approach for solving complex FSI problems in 3D. Copyright © 2011 John Wiley & Sons, Ltd.     

A parallel iterative partitioned coupling analysis system for large-scale acoustic fluid–structure interactions

In many engineering fields, dynamic response in fluid–structure interaction (FSI) is important, and some of the FSI phenomena are treated as acoustic FSI (AFSI) problems. Dynamic interactions between fluids and structures may change dynamic characteristics of the structure and its response to external excitation parameters such as seismic loading. This paper describes a parallel coupling analysis system for large-scale AFSI problems using iterative partitioned coupling techniques. We employ an open source parallel finite element analysis system called ADVENTURE, which adopts an efficient preconditioned iterative linear algebraic solver. In addition, we have recently developed a parallel coupling tool called ADVENTURE_Coupler to efficiently handle interface variables in various parallel computing environments. We also employ the Broyden method for updating interface variables to attain robust and fast convergence of fixed-point iterations. This paper describes key features of the coupling analysis system developed, and we perform tests to validate its performance for several AFSI problems. The system runs efficiently in a parallel environment, and it is capable of analyzing three-dimensional-complex-shaped structures with more than 20 million degrees-of-freedom (DOFs). Its numerical results also show good agreement with experimental results.     

Partitioned vibration analysis of internal fluid‐structure interaction problems

A partitioned, continuum‐based, internal fluid–structure interaction (FSI) formulation is developed for modeling combined sloshing, acoustic waves, and the presence of an initial pressurized state. The present formulation and its computer implementation use the method of localized Lagrange multipliers to treat both matching and non‐matching interfaces. It is shown that, with the context of continuum Lagrangian kinematics, the fluid sloshing and acoustic stiffness terms originate from an initial pressure term akin to that responsible for geometric stiffness effects in solid mechanics. The present formulation is applicable to both linearized vibration analysis and nonlinear FSI transient analysis provided that a convected kinematics is adopted for updating the mesh geometry in a finite element discretization. Numerical examples illustrate the capability of the present procedure for solving coupled vibration and nonlinear sloshing problems. Copyright © 2012 John Wiley & Sons, Ltd.     

A monolithic computational approach to thermo‐structure interaction

In the present work, a monolithic solution approach for thermo‐structure interaction problems motivated by the challenging application of the behaviour of rocket nozzles is proposed. Structural and thermal fields are independently discretised via finite elements. The resulting system of equations is solved via a monolithic thermo‐structure interaction scheme, which is constructed by a block Gauss–Seidel preconditioner in combination with algebraic multigrid methods. The proposed method is tested for four numerical examples, the second Danilovskaya problem, a simplified rocket nozzle configuration, an internally loaded hollow sphere, and a fully three‐dimensional nozzle configuration of a subscale thrust chamber. Good agreement of the numerical results with results from the literature is observed. Furthermore, it is shown that the monolithic solution algorithm can handle the complete range of the parameter spectrum, whereas partitioned algorithms are limited to a certain parameter range only. Moreover, the monolithic algorithm exhibits improved efficiency and robustness compared to partitioned algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of space mapping algorithms for application to partitioned fluid–structure interaction problems

Fluid–structure interactions (FSI) play a crucial role in many engineering fields. However, the computational cost associated with high‐fidelity aeroelastic models currently precludes their direct use in industry, especially for strong interactions. The strongly coupled segregated problem—that results from domain partitioning—can be interpreted as an optimization problem of a fluid–structure interface residual. Multi‐fidelity optimization techniques can therefore directly be applied to this problem in order to obtain the solution efficiently. In previous work, it is already shown that aggressive space mapping (ASM) can be used in this context. In this contribution, we extend the research towards the use of space mapping for FSI simulations. We investigate the performance of two other approaches, generalized space mapping and output space mapping, by application to both compressible and incompressible 2D problems. Moreover, an analysis of the influence of the applied low‐fidelity model on the achievable speedup is presented. The results indicate that output space mapping is a viable alternative to ASM when applied in the context of solver coupling for partitioned FSI, showing similar performance as ASM and resulting in reductions in computational cost up to 50% with respect to the reference quasi‐Newton method. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical study of partitioned fluid-structure interaction applied to a cantilever in incompressible turbulent flow

This study presents an approach for partitioned fluid-structure interaction (FSI) applied to large structural deformations, where an incompressible turbulent solver is combined with a structural solver. The implementation is based upon two different open-source libraries by using MPI as a parallel communication protocol, the packages and OpenFOAM. FSI is achieved through a strongly-coupled scheme. The solver has been validated against cases with a submerged cantilever in a channel flow to which experiments, numerical calculations and theoretical solutions are available. The verification of the procedure is performed by using a solid-solid interaction (SSI) study. The solver has proven to be robust and has the same parallel efficiency as the fluid and the solid solver stand-alone.     

Convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring

In order to predict the dynamic response of a complex system decomposed by computational or physical considerations, partitioned procedures of coupled dynamical systems are needed. This paper presents the convergence analysis of a novel parallel interfield procedure for time‐integrating heterogeneous (numerical/physical) subsystems typical of hardware‐in‐the‐loop and pseudo‐dynamic tests. The partitioned method is an extension of the method originally proposed by Gravouil and Combescure which utilizes a domain decomposition enforcing the continuity of the velocity at interfaces. In particular, the merits of the new method which can couple arbitrary Newmark schemes with different time steps in different subdomains and advance all the substructure states simultaneously are analysed in terms of accuracy and stability. All theoretical results are derived for single‐ and two‐degrees‐of‐freedom systems, as a multi‐degree‐of‐freedom system is too difficult to analyse mathematically. However, the insight gained from the analysis of these coupled problems and the conclusions drawn are confirmed by means of the numerical simulation on a four‐degrees‐of‐freedom system. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of fluid–structure interactions using a velocity‐linked P2/P1 finite element method and the generalized‐ α method

A velocity‐linked algorithm for solving unsteady fluid–structure interaction (FSI) problems in a fully coupled manner is developed using the arbitrary Lagrangian–Eulerian method. The P2/P1 finite element is used to spatially discretize the incompressible Navier–Stokes equations and structural equations, and the generalized‐ α method is adopted for temporal discretization. Common velocity variables are employed at the fluid–structure interface for the strong coupling of both equations. Because of the velocity‐linked formulation, kinematic compatibility is automatically satisfied and forcing terms do not need to be calculated explicitly. Both the numerical stability and the convergence characteristics of an iterative solver for the coupled algorithm are investigated by solving the FSI problem of flexible tube flows. It is noteworthy that the generalized‐ α method with small damping is free from unstable velocity fields. However, the convergence characteristics of the coupled system deteriorate greatly for certain Poisson's ratios so that direct solvers are essential for these cases. Furthermore, the proposed method is shown to clearly display the advantage of considering FSI in the simulation of flexible tube flows, while enabling much larger time‐steps than those adopted in some previous studies. This is possible through the strong coupling of the fluid and structural equations by employing common primitive variables. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydroelastic analysis of insulation containment of LNG carrier by global–local approach

The insulation containment of liquefied natural gas (LNG) carriers is a large‐sized elastic structure made of various metallic and composite materials of complex structural composition to protect the heat invasion and to sustain the hydrodynamic pressure. The goal of the present paper is to present a global–local numerical approach to effectively and accurately compute the local hydroelastic response of a local containment region of interest. The global sloshing flow and hydrodynamic pressure fields of interior LNG are computed by assuming the flexible containment as a rigid container. On the other hand, the local hydroelastic response of the insulation containment is obtained by solving only the local hydroelastic model in which the complex and flexible insulation structure is fully considered and the global analysis results are used as the initial and boundary conditions. The interior incompressible inviscid LNG flow is solved by the first‐order Euler finite volume method, whereas the structural dynamic deformation is solved by the explicit finite element method. The LNG flow and the containment deformation are coupled by the Euler–Lagrange coupling scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

A hybrid variational Allen-Cahn/ALE scheme for the coupled analysis of two-phase fluid-structure interaction

We present a partitioned iterative formulation for the modeling of fluid-structure interaction (FSI) in two-phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz, an incompressible viscous fluid, a rigid or flexible structure, and a two-phase indicator field. The fluid-fluid interface between the two phases, which may have high density and viscosity ratios, is evolved by solving the conservative phase-field Allen-Cahn equation in the arbitrary Lagrangian-Eulerian coordinates. While the Navier-Stokes equations are solved by a stabilized Petrov-Galerkin method, the conservative Allen-Cahn phase-field equation is discretized by the positivity preserving variational scheme. Fully decoupled implicit solvers for the two-phase fluid and the structure are integrated by the nonlinear iterative force correction in a staggered partitioned manner and the generalized-α method is employed for the time marching. We assess the accuracy and stability of the phase-field/ALE variational formulation for two- and three-dimensional problems involving the dynamical interaction of rigid bodies with free surface. We consider the decay test problems of increasing complexity, namely, free translational heave decay of a circular cylinder and free rotation of a rectangular barge. Through numerical experiments, we show that the proposed formulation is stable and robust for high density ratios across fluid-fluid interface and for low structure-to-fluid mass ratio with strong added-mass effects. Overall, the proposed variational formulation produces results with high accuracy and compares well with available measurements and reference numerical data. Using unstructured meshes, we demonstrate the second-order temporal accuracy of the coupled phase-field/ALE method via decay test of a circular cylinder interacting with the free surface. Finally, we demonstrate the three-dimensional phase-field FSI formulation for a practical problem of internal two-phase flow in a flexible circular pipe subjected to vortex-induced vibrations due to external fluid flow.     

Numerical analysis of blast-induced wave propagation using FSI and ALEmulti-material formulations

As explosive blasts continue to cause casualties in both civil and military environments, there is a need to identify the dynamic interaction of blast loading with structures, to know the shock mitigating mechanisms and, most importantly, to identify the mechanisms of blast trauma. This paper examines the air-blast simulation using Arbitrary Lagrangian Eulerian (ALE) multi-material formulation. It will explain how the fluid–structure interaction (FSI) can be simulated using a coupling algorithm for the treatment of the fluid as a moving media by a moving mesh using ALE formulation and how the structure is treated on a deformable mesh using a Lagrangian formulation. To validate the numerical approach, as well as to prove its ability to simulate complicated scenarios, comparison of three distinct blast scenarios, i.e., blast from C-4 and TNT in open space and blast on a circular steel plate, with the experimental data was performed. The predicted numerical results match very well with those of experiments. This computational approach is able to accurately predict the relevant aspects of the blast–structure interaction problem, including the blast wave propagation in the medium and the response of the structure to blast loading.     

Fluid–structure interaction problems with strong added‐mass effect

In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid–structure interaction problems, which has good convergent characteristics even for biomechanical application, where the added‐mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods. Copyright © 2009 John Wiley & Sons, Ltd.     

ITERATIVE SOLUTION OF COUPLED FE/BE DISCRETIZATIONS FOR PLATE–FOUNDATION INTERACTION PROBLEMS

In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate–foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.     

Fluid–structure interaction modeling of wind turbines: simulating the full machine

In this paper we present our aerodynamics and fluid?Cstructure interaction (FSI) computational techniques that enable dynamic, fully coupled, 3D FSI simulation of wind turbines at full scale, and in the presence of the nacelle and tower (i.e., simulation of the ??full machine??). For the interaction of wind and flexible blades we employ a nonmatching interface discretization approach, where the aerodynamics is computed using a low-order finite-element-based ALE-VMS technique, while the rotor blades are modeled as thin composite shells discretized using NURBS-based isogeometric analysis (IGA). We find that coupling FEM and IGA in this manner gives a good combination of efficiency, accuracy, and flexibility of the computational procedures for wind turbine FSI. The interaction between the rotor and tower is handled using a non-overlapping sliding-interface approach, where both moving- and stationary-domain formulations of aerodynamics are employed. At the fluid?Cstructure and sliding interfaces, the kinematic and traction continuity is enforced weakly, which is a key ingredient of the proposed numerical methodology. We present several simulations of a three-blade 5~MW wind turbine, with and without the tower. We find that, in the case of no tower, the presence of the sliding interface has no effect on the prediction of aerodynamic loads on the rotor. From this we conclude that weak enforcement of the kinematics gives just as accurate results as the strong enforcement, and thus enables the simulation of rotor?Ctower interaction (as well as other applications involving mechanical components in relative motion). We also find that the blade passing the tower produces a 10?C12?% drop (per blade) in the aerodynamic torque. We feel this finding may be important when it comes to the fatigue-life analysis and prediction for wind turbine blades.     

Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves

This paper presents a novel numerical method for simulating the fluid?Cstructure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.     

Preliminary results on acoustic modelling of cavitating propellers

The numerical prediction of the acoustic pressure field induced by cavitating marine propellers is addressed. A hydrodynamic model for transient sheet cavitation on propellers in non–uniform inviscid flow is coupled with a hydroacoustic model based on the Ffowcs Williams–Hawkings equation. The proposed hydroacoustic approach, novel to marine applications, allows to split the noise signature into thickness and loading term contributions. Both hydrodynamic and hydroacoustic model equations are solved via boundary integral formulations. Numerical predictions of the propeller noise by using the Ffowcs Williams–Hawkings equation are compared to those obtained by a classical Bernoulli equation approach. The influence of cavitation on the noise waveforms is discussed by comparing non–cavitating and cavitating propeller flow results. The authors wish to thank Prof. S.A. Kinnas for providing a detailed documentation of the experiment used as the test case in the present analysis. The present work was supported by the Ministero dei Trasporti e della Navigazione in the frame of INSEAN Research Program 2000–02.     

Immersed smoothed finite element method for two dimensional fluid–structure interaction problems

A novel method called immersed smoothed FEM using three‐node triangular element is proposed for two‐dimensional fluid–structure interaction (FSI) problems with largely deformable nonlinear solids placed within incompressible viscous fluid. The fluid flows are solved using the semi‐implicit characteristic‐based split method. Smoothed FEMs are employed to calculate the transient responses of solids based on explicit time integration. The fictitious fluid with two assumptions is introduced to achieve the continuous form of the FSI conditions. The discrete formulations to calculate the FSI forces are obtained in terms of the characteristic‐based split scheme, and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the FSI force exerted on the solid. The accuracy, stability, and convergence properties of immersed smoothed FEM are verified by numerical examples. Investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio. No additional volume correction is required to satisfy the incompressible constraints. Copyright © 2012 John Wiley & Sons, Ltd.