Method For Fluid-structure Interaction Problems Research Articles

An efficient partitioned framework to couple Arbitrary Lagrangian-Eulerian and meshless vector form intrinsic finite element methods for fluid-structure interaction problems with deformable structures

The Vector Form Intrinsic Finite Element (VFIFE) is an advanced meshless Lagrangian structural solver. This study introduces a partitioned framework to integrate Arbitrary Lagrangian-Eulerian and VFIFE methods into fluid-structure interaction (FSI) problems featured by large structural displacements and deformations. The VFIFE method enables the FSI simulations with deformable structures due to the nature of Lagrangian particles, which is challenging for traditional computational fluid mechanics techniques. In addition, the VFIFE can be effectively equipped with the partitioned coupling schemes because of the versatility of governing equations. In this algorithm system, several matrix problems in finite element methods and mapping and interpolation in the fluid-structure interface can be avoided. The significant potential of this algorithm in tackling complex FSI problems is demonstrated through various benchmarks, encompassing scenarios like Taylor-Green vortex, flow over a rigid cylinder (Re = 40 ∼ 200), forced vibration of a rigid cylinder, vortex-induced vibration (VIV) of an elastically mounted cylinder, and VIV of a rigid cylinder with an attached flexible cantilever beam. Finally, an experiment on flow past a curtain in a water tank is conducted to further evaluate the precision and stability of the current coupling strategy in three dimensions, demonstrating the feasibility of such methods in flexible structures.

Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems

In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin–Temam projection scheme is applied to the incompressible Navier–Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid. The coupled problem is based on an Arbitrary Lagrangian Eulerian formulation, and the Proper Orthogonal Decomposition procedure is used for the generation of the reduced basis. We extend existing works on a segregated Reduced Order Model for Fluid-Structure Interaction to unsteady problems that couple an incompressible, Newtonian fluid with a linear elastic solid, in two spatial dimensions. We consider three test cases to assess the overall capabilities of the method: an unsteady, non-parametrized problem, a problem that presents a geometrical parametrization of the solid domain, and finally, a problem where a parametrization of the solid’s shear modulus is taken into account.

Time-adaptive partitioned method for fluid-structure interaction problems with thick structures

In this paper, we present a partitioned numerical scheme for solving fluid-structure interaction (FSI) problems based on the adaptive time-stepping. The viscous, incompressible fluid is described using the Navier-Stokes equations expressed in an Arbitrary Lagrangian Eulerian (ALE) form while the elastic structure is modeled using elastodynamic equations. We implement a partitioned scheme based on the Robin-Robin coupling conditions at the interface, combined with the refactorization of Cauchy's one-legged θ-like method with adaptive time-stepping. The method is unconditionally stable, and for θ=12, it corresponds to the midpoint rule, which is conservative and second-order convergent in time. The focus of this paper is to study the time-adaptivity properties of the proposed method, and to explore the parameters used in the variable time-stepping. The adaptive process is based on the local truncation error (LTE), for computation of which we consider two methods: Milne's device using a modified Adams-Bashforth two-step method, and Taylor's method. The performance of the method is explored in numerical examples, where the adaptive approach is compared to the one where a fixed time step is used. We present an example based on the method of manufactured solutions, where the effect of different parameters is studied, followed by a classical benchmark problem of a flow around a rigid cylinder attached to a nonlinearly elastic bar inside a two-dimensional channel. Finally, we present a three-dimensional, simplified example of blood flow in a compliant artery.

A Lagrangian Point Approximation-Based Immersed Boundary–Lattice Boltzmann Method for FSI Problems Involving Deformable Body

The proposed immersed boundary-lattice Boltzmann method (IB-LBM) with smoothed point interpolation method (S-PIM) has been verified to be an effective tool for simulating complex fluid–structure interaction (FSI) problems in previous works. LBM is employed as fluid solver with a simple solution process, S-PIM is used for largely deformable solids on the basis of gradient smoothing technique, and their combinations for FSI problems are achieved under the framework of immersed boundary method (IBM). IBM allows the coupling method to use a fixed fluid Euler mesh to avoid frequent mesh updates due to the movement or deformation of solids, whereas the introduction of fictitious fluid causes the internal mass effect and yields numerical errors. An extended Lagrangian point approximation approach has been proposed and introduced in IB-LBM with S-PIM to tackle this issue, and numerical experiments for FSI problems associated with rigid movement and large deformation of solids are investigated. It is verified that the accuracy and convergency properties of the present method are significantly improved compared with the original one in which the mass effect was not considered.

A special numerical method for fluid-structure interaction problems subjected to explosion and impact loading

A three-dimensional (3D) embedded Eulerian-Lagrangian method is proposed to simulate the 3D fluid-structure interaction (FSI) problems subjected to explosion and impact loading. This method achieves a high-quality calculation of fluid and structure deformation by adding Lagrangian particles to Eulerian grids. The overall computational domain is solved by the Eulerian method, and the Lagrangian particles with specified volume and influence domains are used to track structural deformations. The bidirectional mapping of physical quantities is achieved using the weighted average of the influence domain, which are based on the topological relationship between Eulerian grids and Lagrangian particles. Then, the data dependence solution and parallel algorithm realization are presented for the large-scale numerical calculations of explosion and impact problems. Additionally, the corresponding parallel program is developed based on the message passing interface (MPI) standard, and the parallel efficiency of parallel hydrocode are tested. The numerical results of typical explosion and impact problems are compared with corresponding experimental data to verify the effectiveness of the method. These comparisons show that the embedded Eulerian-Lagrangian method successfully combine the advantages of both the Eulerian and Lagrangian methods to efficiently calculate the processes of large deformation and dynamic damage to the materials. The results presented in this work provide a useful reference point for further research on explosion and impact problems.

An immersed boundary-lattice Boltzmann method for fluid-structure interaction problems involving viscoelastic fluids and complex geometries

An immersed boundary-lattice Boltzmann method (IB-LBM) for fluid-structure interaction (FSI) problems involving viscoelastic fluids and complex geometries is presented in this paper. In this method, the fluid dynamics and the constitutive equations of viscoelastic fluids are both solved using the lattice Boltzmann method. In order to enhance numerical stability in solving the constitutive equations, an artificial damping is introduced which does not affect the numerical results if the damping effect is much smaller than the relaxation and the convective effects. The structural dynamics including 2D and 3D capsules, 2D and 3D rigid particles and flags, are solved by the finite difference method (2D capsules, 2D and 3D rigid particles and flags) and the finite element method (3D capsules). The interaction between the solid structure and the fluid is enforced by an immersed boundary method. The overall framework of this method is very simple, enabling modelling FSI problems involving viscoelastic fluids and the inertia of both fluids and structures. It is very efficient for FSI problems involving high Weissenberg numbers flows, large deformations and complicated geometries without any preconditioner. This work uses IB-LBM to solve for the first time, flows involving viscoelastic fluids coupled with non-massless deforming structures. The method is also capable of solving very high Weissenberg number problems, as demonstrated by simulations of flexible particle flows at Wi=100. The present method and models are validated by several cases including a 2D rigid particle migration in a Giesekus Couette flow, a spherical particle rotation in an Oldroyd-B shear flow, a spherical particle settling in a FENE-CR fluid, 2D and 3D capsules deformation in a Newtonian shear flow, and a 3D flag flapping in a Newtonian free stream. In addition, the present method is also applied to simulate the deformation of 2D and 3D capsules in an Oldroyd-B shear flow, a 3D flag flapping in an Oldroyd-B free stream, and elastic capsule movement in a contraction-expansion channel filled with an Oldroyd-B fluid. Deformation of the capsules decreases with the increase of the Weissenberg number and the capsules experience monotonically increasing deformation when the Weissenberg number is above a critical value which is respectively 10 for 2D and 2 for 3D simulations. Viscoelasticity of the Oldroyd-B fluid hinders the flapping motion of the 3D flag. For elastic capsules passing through a periodic contraction-expansion channel, the capsules mix up after a short-term evolution, and then migrate to the bottom of the channel and almost follow two steady trajectories after a long-term evolution. The validations and applications provide extensive data which may be used to expand the currently limited database available for FSI benchmark studies.

A coupled NMM-SPH method for fluid-structure interaction problems

• A coupled NMM-SPH method for fluid-structure interaction problems is present. • The proposed method takes full advantage of NMM for the solid structures and SPH for fluid particles. • A contact algorithm is developed which can handle the interaction between NMM elements and SPH particles well. • Compared to DDA-SPH or DEM-SPH, NMM-SPH can accurately calculate the stress of the structure. • The proposed method can also predict the failure of the solid structure under the action of fluid. The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.

A combined radial basis function based interpolation method for fluid-structure interaction problems and its application on high-speed trains

In fluid-structure interaction (FSI) problems, accuracy of the data transfer between fluid-structure interfaces is mainly attributed to the element type and discretization density of grids in both fluid and structure domains. To remedy the inaccuracy caused by the prevalently applied solo elemental node interpolation strategy, a novel interpolation method is proposed in the present study. The approach is based on the radial basis function and introduces a weight coefficient through which the centroid and nodes of an element are joined. This way, the interpolation will be conducted in accordance to a weighted summation of both terms. Before it is applied to practice relevant engineering examples, the validity of the formulated approach is first examined by simple 2D and further 3D case studies. Studies have clearly illustrated that, compared to pure element centroid or nodes based interpolation schemes, the established approach is insensitive to the pressure distribution. Meanwhile, in these cases the influence of selected basis functions and mesh densities have been examined in detail. Based on the knowledge gained from these case studies, it further investigated a problem emerged from high-speed trains in which the CFD simulation is validated by the field experiment and the task is to transfer data from the fluid domain to the structure domain. Result of the study shows that for the high speed train model considered which has complicated non-matching grids, the accuracy of data transfer in fluid-structure interaction is highly improved and the maximum of global relative error achieves 2.62%.

陽的MPS法とHamiltonian MPS法を用いた3次元流体－構造連成解析手法の開発

陽的MPS法とHamiltonian MPS法を用いた3次元流体－構造連成解析手法の開発

K02300 超大規模並列計算に適した流体・構造連成解析手法の開発

K02300 超大規模並列計算に適した流体・構造連成解析手法の開発

A Simulation Method for Fluid-Structure Interaction Problems with Free Surface based on the Finite Cover Method

This paper presents a new Eulerian type numerical method for Fluid-Structure Interaction (FSI) problems with free surface based on the finite cover method (FCM). Since the physical domain is defined independently of the mathematical domain in the FCM, which is known as a generalized version of the FEM, the physical boundaries of the structure are represented explicitly in a spatially fixed mesh so that the continuity condition can be imposed directly on the actual interface within the framework of Eulerian approach. The VOF and Level Set method are employed to represent interfaces, and the stabilized method based on the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods are employed for flow analysis. The weak coupling scheme is employed for the interaction between fluid and structure. The proposed method is applied to several numerical examples to show the validity and efficiency of the method.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

Domain decomposition based Newton methods for fluid-structure interaction problems

We review various fluid-structure algorithms based on domain decomposition techniques and we propose a new one. The standard methods used in fluid-structure interaction problems are generally on subdomains. We propose a scheme based on the principle linearize first, then decompose. In other words we extend to fluid-structure problems domain decomposition techniques classically used in nonlinear elasticity. Resume. Nous faisons une revue de divers algorithmes de couplage fluide-structure bases sur des tech- niques de decomposition de domaine et nous en proposons une nouvelle. Les methodes classiquement utilisees en interaction fluide-structure sont generalement lineaires par sous-domaine. Le schema que nous proposons est au contraire base sur le principe lineariser puis decomposer. Autrement dit, nousetendons aux problemes d'interaction fluide-structure des techniques de decomposition de domaine classiquement utilisees enelasticite non lineaire.

Flow Characteristics in Elastic Arteries Using a Fluid-Structure Interaction Model

In this study the interaction of blood flow with arterial wall has been investigated using FSI (Fluid-Structure Interaction) modeling. Computer simulation of pulsatile blood flow was carried out on the basis of the time dependent axisymmetric Navier-Stokes equations for an incompressible Newtonian fluid flow. An elastic incompressible material with large deformation was considered for the arterial wall and momentum and continuity equations of elastodynamics have been solved. The specified boundary conditions for the Navier-Stokes equations were the pulsatile pressure waveforms of the brachial artery at inflow and outflow to the given pulse wave form of a cardiac cycle. Fluid and solid equations were solved with the ALE-based loose coupling method for FSI problems. Resultant flow, wall displacement, wall shear stress and wall circumferential strain waves, and their phase differences were determined. Stiffening of the arterial wall resulted in a significant decrease in the mean values of flow and wall shear stress and altered waveforms. A tenfold increase in wall stiffness caused 33% drop in flow and negative values of shear stress in 21% of the pressure pulse. For elastic moduli corresponding to wall displacements less than 1% the blood flow and wall shear stress were not sensitive to wall stiffness. Stress phase angle was altered by stiffening of the arterial wall. It was concluded that FSI modeling with pressure boundary conditions provides a proper evaluation of hemodynamic parameters that may determine endothelial injury.

A LEVEL SET METHOD FOR FLUID-STRUCTURE INTERACTIONS WITH IMMERSED SURFACES

This paper is devoted to the derivation and the validation of a level set method for fluid-structure interaction problems with immersed surfaces. The test case of a pressurized membrane is used to compare our method to Peskin's Immersed Boundary methods in the two-dimensional case and to demonstrate its capabilities for three-dimensional flows. The method in particular exhibits appealing mass and energy conservation properties.

Least squares finite element methods for fluid-structure interaction problems

The first order least squares finite element method is an alternative numerical procedure to standard Galerkin methods for the solution of partial differential equations. Its advantages are mainly the resulting symmetric positive definite matrices and the inherent numerical stability. Several first order formulations were proposed for the incompressible Navier–Stokes equations and for the equations of linear elasticity. Here we analyse which of these methods could provide an efficient and accurate tool for the solution of fluid-structure interaction problems. It seems that the combination of inherent least squares stability and high order ansatz functions is very promising.

Possibilities of the particle finite element method for fluid-structure interaction problems with free surface waves

We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

Finite-element-based computational methods for cardiovascular fluid-structure interaction

In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.

A data exchange method for fluid-structure interaction problems

AbstractThis paper presents and illustrates an interpolation method for the exchange of displacement data between fluid and structural meshes in a fluid-structure interaction simulation. The method is a local method where element volume conservation is central, and does not rely on information from the structural model. Results are evaluated for several two and three dimensional problems. Comparisons with the infinite plate spline method show that the new method gives a more realistic representation of the recovered surface than currently used methods.