Fluid-structure Interface Research Articles

A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem

AbstractA finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.

Hydroelastic linearized vibrations taking into account prestressed effects due to internal liquid weight: Numerical vs. experimental results

This paper concerns the numerical simulation of the hydroelastic vibrations of an elastic tank containing a free surface liquid, around a geometrically nonlinear equilibrium configuration that takes into account the prestress effect due to the liquid weight. The computational methodology is the following. Firstly, the hydrostatic pressure on the fluid–structure interface is considered as a non-uniform follower force which depends on the liquid height. Therefore, the prestressed equilibrium at a given free-surface level, called current configuration in the paper, is computed as a geometrically nonlinear problem, in which the height of the liquid is considered as an evolution parameter. We start from an empty structure, defined as the reference configuration, which is progressively filled to reach the level of the chosen configuration. Therefore the calculation of hydroelastic vibrations of a tank filled with liquid as a function of a emptying rate is straightforward. The methodology is validated with experimental results extracted from literature.

An immersed MMALE material point method for FSI problems with structure fracturing

The fluid–structure-interaction (FSI) modeling is important for both academic studies and engineering applications, but is also one of the grand challenges in the numerical modeling community. The FSI problems with multi-material fluid flow and extreme structure deformation accompanied with fractures and crack growth are less explored areas. In these problems, the interface reconstruction, multi-material advection, interface interaction on the complicated fluid structure interface and potential structure fragmentation must be all taken into account. This paper aims to present an effective monolithic approach of immersed multi-material arbitrary Lagrangian Eulerian material point method (IALEMPM) by immersing the MPM particles in the MMALE grid. In this novel method, the interfaces between the fluid and structure are tracked implicitly by the MPM particles and the interface interactions are implicitly implemented by assembling the nodal force and the nodal momentum from both the solid particles and fluid cells. The consistence time integration scheme, rezoning phase and remapping phase are also established to guarantee the consistence requirements during the whole simulation. Numerical examples, including a shock-obstacle interaction, a blast-plate interaction and a structure fragmentation are studied by using the IALEMPM, and all the numerical results show good agreement with the benchmark and the experiment data, which indicates that the IALEMPM is effective for solving these complicated FSI problems.

Moving Particle Semi-implicit method coupled with Finite Element Method for hydroelastic responses of floating structures in waves

In this paper, the Moving Particle Semi-implicit (MPS) method and Finite Element Method (FEM) coupling computational method is applied to solve the problem of hydroelastic response of floating structures. The MPS method, a Lagrangian meshfree method, is suitable for simulating violent flows such as breaking waves on free surface. For a floating structure like the ship hull and floating breakwater, the typical feature of motion is a large rigid-body motion plus a relatively small deformation. Therefore, a rigid–flexible coupling strategy based on MPS–FEM coupled method is developed. According to the choice of structural element, appropriate data transformation schemes are adopted on the fluid–structure interface. In this paper, the grouping exchange technique is developed, which is applied on the interface of particle model-beam element. The reliability of present method is verified through simulations of fluid–structure interaction (FSI) problems including water entry of the elastic wedge, water entry of the marine panel and dam-break wave impacting on a mooring flexible platform, the obtained numerical result is in good agreement with the published data. Afterwards, the coupling of fluid and structure solver is also tested by various problems including the cases of three-dimensional deformable floating platform/ship slamming in waves.

Spline-based space-time finite element approach for fluid-structure interaction problems with a focus on fully enclosed domains

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible to use such NURBS geometries for numerical analysis directly. Analyzing fluid flows, however, requires complex three-dimensional geometries to represent flow domains. Defining a parametrization of such volumetric domains using NURBS can be challenging and is still an ongoing topic in the IGA community.With the recently developed NURBS-enhanced finite element method (NEFEM), the favorable geometric characteristics of NURBS are used within a standard finite element method. This is achieved by enhancing the elements touching the boundary by using the NURBS geometry itself. In the current work, a new variation of NEFEM is introduced, which is suitable for three-dimensional space-time finite element formulations. The proposed method makes use of a new mapping which results in a non-Cartesian formulation suitable for fluid-structure interaction (FSI).This is demonstrated by combining the method with an IGA formulation in a strongly-coupled partitioned framework for solving FSI problems. The framework yields a fully spline-based representation of the fluid-structure interface through a single NURBS.The coupling conditions at the fluid-structure interface are enforced through a Robin-Neumann type coupling scheme. This scheme is particularly useful when considering incompressible fluids in fully Dirichlet-bounded and curved problems, as it satisfies the incompressibility constraint on the fluid for each step within the coupling procedure.The accuracy and performance of the introduced spline-based space-time finite element approach and its use within the proposed coupled FSI framework are demonstrated using a series of two- and three-dimensional benchmark problems.

A dynamic substructuring technique for coupling and decoupling structure-cavity systems

Flexible structures adjacent to acoustic cavities are commonly encountered. In some instances, coupling between the structure and cavity causes non-negligible changes to the system frequency response. Here, we describe the use of modern dynamic substructuring techniques in coupling and decoupling structure-cavity systems. As input, free-interface in vacuo natural frequencies and modes of the structure are used along with an uncoupled modal representation of the cavity. In the acoustic model, the fluid-structure interface is typically modeled as pressure release, though faster frequency convergence is possible by enriching the representation with rigid-wall modes. The subsystems are assembled in modal coordinates with continuity at the interface enforced via Lagrange multipliers. This approach circumvents the calculation of coupling coefficients, and results in real-valued system natural frequencies and modes; however, the approach presents challenges when large numbers of interface degrees of freedom are present. Attempts to overcome these challenges with interface reduction techniques are described. Finally, this research led to the derivation of a formula approximating the in vacuo natural frequencies of test structures that are well coupled to adjacent acoustic cavities. The formula was successfully applied to an air-filled cylindrical test structure for which the frequency response was confounded by structure-cavity coupling.

Vibration analysis of functionally graded porous cylindrical shells filled with dense fluid using an energy method

In this paper, a novel energy approach is proposed for fully coupled fluid-structure problems of functionally graded porous (FGP) fluid-filled cylindrical shells under arbitrary boundary conditions. Kinds of continuous FG materials are considered including various patterns in which the voids distributed. A modified variational principle is developed in fluid domain as well as in structural domain, naturally reinforcing the restrains on the boundaries and interfaces between adjacent subdomains. Energy functions in structural and fluid domain are deduced based on the first-order shear deformable shell theory (FSDT) and Helmholtz equation, respectively. The fluid-structure interactions are successfully introduced with the work done by the sound pressure and displacement continuous conditions at fluid-structural interface. A semi-analytical solution is obtained by expanding the displacement and sound pressure components analytically in the circumferential direction and numerically in the axial direction. Good convergence, high accuracy, superior efficiency and flexibility in using admissible functions are demonstrated by comparing reasonably many proposed results with those in literatures or obtained by FEM/BEM. Numerous examples are developed to examine the effects of material properties and boundary conditions on free vibration of FGP cylindrical shells with and without water. With added mass factor introduced, the influences of the key parameters on the fluid-structure coupling are also presented. The slight dependences of the added mass factor on material and boundary conditions greatly broaden the applied scope of the numerical results.

An immersed finite element material point (IFEMP) method for free surface fluid–structure interaction problems

The inherent nonlinearity of free surface fluid–structure interaction (FSI) problems challenges numerical methods in terms of efficiency and fidelity. In this article, we propose an immersed finite element material point method for the water entry fluid–structure interaction problems. In this method, the fluid domain is discretized by an improved incompressible material point method (iMPM) using both Eulerian and Lagrangian descriptions, while the solid domain is solved by finite element method (FEM). The interaction between the iMPM and FEM is handled by a sharp immersed interface approach. Moreover, weighted tracing points are designed to track the fluid–structure interface with a low time complexity; a particle rearranging method is developed to eliminate the numerical cavities, which are non-physical voids caused by the highly disordered particle distribution, from which the original iMPM for FSI problems suffers. Various free surface FSI problems are presented to demonstrate the accuracy and effectiveness of the proposed method. The computational results are compared with analytical, experimental, and simulation data from the literature, with good agreement in cases where such data is available. The proposed method is expected to be a powerful tool for free surface FSI problems.

MPS–FEM coupled method for 3D dam-break flows with elastic gate structures

In this paper, the MPS–FEM coupled method is applied for the three-dimensional (3D) dam-break flow with elastic gate, where the Moving Particle Semi-implicit (MPS) method and the Finite Element Method (FEM) are respectively used to solve fluid flows and structure deformation. A partitioned coupling strategy of traditional Conventional Serial Staggered (CSS) strategy is employed for MPS method and FEM method coupling. An interfacial data interpolation module called three-dimensional Kernel Function Based Interpolation Technique (3D-KFBI) is developed for the three-dimensional fluid–structure interface. Based on the MPS–FEM​ coupled method, a self-developed MPSFSI solver is developed. Then, the stability, accuracy, convergence and energy conservation properties of the developed data interpolation algorithm is validated by two cases. Afterwards, the proposed coupled method is applied for the case of dam-break flow interacting with the elastic gate. A good agreement between present numerical result and published experiment data Antoci et al. (2007) demonstrates the accuracy and efficiency of the present coupled method. At last, MPSFSI solver is applied for the problem of the narrow dam-break flow with the elastic gate to investigate the three-dimensional effect.

Fluid–structure interaction with ALE formulation and skeleton-based structural models

This paper presents a fluid–structure interaction (FSI) framework that combines an Arbitrary Lagrangian–Eulerian (ALE) formulation with skeleton-based structural models consisting of force-based frame elements. For the first time in literature, a methodology is proposed to enable coupling between fluid and force-based frame elements through an ALE formulation. In the proposed methodology, communication between the fluid and skeleton-based domains is performed through a geometric model of the physical fluid–structure interface. With the use of force-based frame elements, the intent is to perform accurate FSI calculations in cases where axial, flexure, and shear motions dominate the structural responses. The proposed framework is evaluated against FSI problems involving steady and unsteady incompressible laminar flows and different structural models representing horizontal (beam) and vertical (column) solid members.

A linearized ALE Boundary Element Method for flexible 3D bluff bodies in potential flows: Towards application to airship aeroelasticity

Effects of fluid–structure coupling on the dynamic behavior of flexible airships can be modeled with a potential, incompressible, inviscid flow. A new formalism to study the linear behavior of a fluid–structure interface in a time-dependent ambient flow is introduced. The fluid equations are condensed at the interface with the help of integral equations, which are expressed as a function of the structure variables defined on a time-independent reference configuration with an Arbitrary Lagrangian–Eulerian (ALE) formalism. The features of the Boundary Element Method (BEM) used to solve this problem numerically are exhibited. The approximations of this method associated with both linearization and discretization are quantified to validate the model. A simplified flexible airship test case model is studied to illustrate a practical application of the method.

Splitting schemes for the stress formulation of fluid–structure interaction problems

In this article we demonstrate that the novel stress formulation of the Navier–Stokes equations proposed in Minev and Vabishchevich (2018) can be extended to the case of fluid–structure interaction problems. This formulation allows for an easy treatment of the fluid–structure interface boundary conditions. Furthermore, we propose a first order (in time) splitting scheme for this formulation and study its stability in the linear case. It utilizes a level set approach for the interface tracking and regularization of the interface problem. We also demonstrate how this scheme can be extended to the nonlinear case of a neo-Hookean elastic material. The computational complexity of the resulting problem seem to be comparable or better than most available schemes that treat the problem in primitive variables. A downside of such an approach is that it requires a higher than the traditional formulations in terms of primitive unknowns degree of smoothness of the solution for the stress. However, in addition to the solution for the velocity and the stress, it also yields information about the stress tensor, computed with an optimal accuracy.The scheme is demonstrated on two benchmark problems borrowed by other authors, and the results, although computed with a purely linear model look very similarly to the results of other authors that are based on a nonlinear neo-Hookean model.

A strongly coupled immersed boundary method for fluid-structure interaction that mimics the efficiency of stationary body methods

Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large dimensional systems that scale by the number of grid points in the flow domain even though the nonlinear constraints scale only by the small number of points used to represent the fluid-structure interface. These costly large scale operations for determining only a small number of unknowns at the interface creates a bottleneck to efficiently time-advancing strongly coupled IB methods. In this manuscript, we present a remedy for this bottleneck that is motivated by the efficient strategy employed in stationary-body IB methods while preserving the favorable stability properties of strongly coupled algorithms—we precompute a matrix that encapsulates the large dimensional system so that the prohibitive large scale operations need not be performed at every time step. This precomputation process yields a modified system of small-dimensional constraint equations that is solved at minimal computational cost while time advancing the equations. We also present a parallel implementation that scales favorably across multiple processors. The accuracy, computational efficiency and scalability of our approach are demonstrated on several two dimensional flow problems. Although the demonstration problems consist of a combination of rigid and torsionally mounted bodies, the formulation is derived in a more general setting involving an arbitrary number of rigid, torsionally mounted, and continuously deformable bodies.

Failure analysis for concrete gravity dam subjected to underwater explosion: A comparative study

The failure analysis of concrete gravity dams subjected to noncontact underwater explosions (UNDEXs) plays a significant role in evaluating the safety of dams. In this paper, two types of numerical models were developed to predict the failure behavior of a typical concrete gravity dam, i.e., the fully-coupled and semi-coupled model, which can provide a cross validation of the analysis results. The two models were verified by the experimental data and then adopted for the failure analysis. The results show that the shock wave can produce peak value in the blast responses and concentrated damage directly opposite to the explosive source. Even after the energy transmission at the fluid–structure interface, the UNDEX load still had influence on the failure behavior of the dam and can induce a total swelling in the velocity response.

Intelligent Design Optimization System for Additively Manufactured Flow Channels Based on Fluid-Structure Interaction.

Based on expert system theory and fluid–structure interaction (FSI), this paper suggests an intelligent design optimization system to derive the optimal shape of both the fluid and solid domain of flow channels. A parametric modeling scheme of flow channels is developed by design for additive manufacturing (DfAM). By changing design parameters, a series of flow channel models can be obtained. According to the design characteristics, the system can intelligently allocate suitable computational models to compute the flow field of a specific model. The pressure-based normal stress is abstracted from the results and transmitted to the solid region by the fluid–structure (FS) interface to analyze the strength of the structure. The design space is obtained by investigating the simulation results with the metamodeling method, which is further applied for pursuing design objectives under constraints. Finally, the improved design is derived by gradient-based optimization. This system can improve the accuracy of the FSI simulation and the efficiency of the optimization process. The design optimization of a flow channel in a simplified hydraulic manifold is applied as the case study to validate the feasibility of the proposed system.

A parallel domain decomposition algorithm for fluid-structure interaction simulations of the left ventricle with patient-specific shape

<abstract> <p>In this paper, we propose a scalable parallel algorithm for simulating the cardiac fluid-structure interactions (FSI) of a patient-specific human left ventricle. It provides an efficient forward solver to deal with the induced sub-problems in solving an inverse problem that can be used to quantify the interested parameters. The FSI between the blood flow and the myocardium is described in an arbitrary Lagrangian-Eulerian (ALU) framework, in which the velocity and stress are assumed being continuous across the fluid-structure interface. The governing equations are discretized by using a finite element method and a fully implicit backward Eulerian formula, and the resulting algebraic system is solved by using a parallel Newton-Krylov-Schwarz algorithm. We numerically show that the algorithm is robust with respect to multiple model parameters and scales well up to 2300 processor cores. The ability of the proposed method to produce qualitatively true prediction is also demonstrated via comparing the simulation results with the clinic data.</p> </abstract>

A Lagrangian fluid–structure interaction approach for the simulation of airbag deployment

The numerical simulation of airbags is receiving an increasing attention for the remarkable advantages in terms of cost, efficiency, flexibility and amount of data that can be extracted from the analysis. This work proposes an advanced fluid–structure interaction (FSI) numerical technique for the simulation of airbag deployment. The fluid subproblem, described by weakly compressible Navier–Stokes equations, is solved exploiting the advanced features of the Particle Finite Element Method (PFEM) while the solid subproblem is addressed using standard Finite Element method. A domain decomposition approach with a special treatment of the fluid–structure interface conditions has been implemented to couple fluid and structural solvers allowing for non-conforming meshes at the interface and different time step size in the two subdomains. A peculiar feature of the proposed methodology is the explicit time integration, mandatory for the solution of very fast dynamics problems, like the airbag deployment: an explicit fluid solver is coupled explicitly with an explicit structural solver. The proposed technique is first tested on a inflation of a balloon, showing very good agreements and then it has been applied to the real case of airbag deployment.

Numerical Simulation of Bidirectional Flow and Solid Coupling of Single Pile and Single Row Pile Column and Wave

The three-dimensional model of the wave and pile structure was established by using Ansysworkbench software. The bidirectional fluid-structure interaction between the pile and wave was simulated by using Stokes wave theory and the Volume of Fluid Method. The pressure distribution diagram of the fluid-structure interface and the pile structure were observed and analyzed. The maximum equivalent stress on the pile was studied and its variation range was obtained. Compared with Von Mises yield criterion, it was concluded that the pile was stable under such wave conditions.

Regularity of a weak solution to a linear fluid-composite structure interaction problem

In this manuscript, we deal with the regularity of a weak solution to the fluid-composite structure interaction problem introduced in [12]. The problem describes a linear fluid-structure interaction between an incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh-like elastic structure. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic boundary coupling conditions describing continuity of velocity and balance of contact forces at the fluid-structure interface. In [12], it is shown that there exists a weak solution to the described problem. By using the standard techniques from the analysis of partial differential equations we prove that such a weak solution possesses an additional regularity in both time and space variables for initial and boundary data satisfying the appropriate regularity and compatibility conditions imposed on the interface.

Coupling of the meshless finite volume particle method and the finite element method for fluid–structure interaction with thin elastic structures

A novel fluid–structure interaction (FSI) scheme is developed in this article, with the meshless finite volume particle method (FVPM) for fluid dynamics and the finite element (FE) solver FEBio for solid mechanics. Like smoothed particle hydrodynamics (SPH), FVPM is based on compactly supported particle kernels, but kernels are interpreted as a partitioning of volume, leading to a scheme with properties of both SPH and classical finite volume methods. Particle methods are advantageous for fluid modelling in FSI of highly deformable structures, as the particles can conform to the dynamic geometry of the fluid–structure interface. In FVPM, in particular, particles are rigorously truncated by boundaries, and the novel FSI scheme incorporates a sharp interface between the fluid and solid. A new method is described which avoids the possibility of unphysical communication between fluid particles separated by a thin structure. The method proposed here ensures that particles interact with the correct neighbour particles and boundaries, regardless of the particle overlap with the thin structure, allowing for particle size that can be chosen independently of structure thickness. The new method is validated for a hydrostatic water column on an elastic plate, a dam-break with elastic gate, a dam-break with a downstream elastic wall, and a 2-D model of a heart valve leaflet. In the latter two cases, the structure thickness is less than the particle diameter by a factor of up to 16. The results agree well with experimental data from the literature for fluid velocity field and solid deformation. Where quantitative data is available, the numerical results converge with decreasing particle size.