Fluid Mesh Research Articles

A fluid–structure interaction method with solid-rigid contact for heart valve dynamics

A computational method is proposed for problems where fluid–structure interaction is combined with solid-rigid contact. This combination is particularly important for the dynamics and impact of heart valves. The Navier–Stokes equation in an Eulerian setting is coupled to a Neo-Hookean solid model using a Lagrangian description. A fictitious domain method extended with a local mesh adaptation algorithm provides the required flexibility with respect to the motion and deformation of the valve. In addition, it ensures the solids ability of sustaining pressures present in the fluid. Making use of the fact that the fluid and solid mesh are not required to be connected conformingly, it is shown that the model can be extended with a contact algorithm without introducing meshing complications near the contact surfaces.

Simulation of the Flow-Induced Acoustic Vibration and Noise Generation in a Multi-Stage Centrifugal Pump

This article reports a full-scale structural simulation of flow-induced mechanical noise in a 5-stage centrifugal pump. An interior flow field is simulated by a LES-based CFD code individually, which can be found elsewhere. This paper focuses on data interface, and a structural vibration analysis. We developed a data interface tool to enable mesh match as well as data interpolation between fluid and structure meshes. The vibration of a structural portion is simulated using a parallel explicit dynamic FE code, providing the time series of fluctuating pressure on internal surface as force boundary conditions. The calculated vibration of outer surface of the structure agrees reasonably well with measured one. By Fourier transformation, the vibration modes at the blade passing frequencies were extracted and visualized. The simulation clarified the mechanisms of resonant noise generation and propagation.

From Immersed Boundary Method to Immersed Continuum Methods

The objective of this paper is to present an overview of the newly proposed immersed continuum method in conjunction with the traditional treatment of fluidstructure interaction problems, the immersed boundary method, the extended immersed boundary method, the immersed finite element method, and the fictitious domain method. In particular, the key aspects of the immersed continuum method in comparison with the immersed boundary method are discussed. The immersed continuum method retains the same strategies employed in the extended immersed boundary method and the immersed finite element method, namely, the independent solid mesh moves on top of a fixed or prescribed background fluid mesh, and employs fully implicit time integration with a matrix-free combination of NewtonRaphson and GMRES iterative solution procedures. Therefore, the immersed continuum method is capable of handling compressible fluid interacting with compressible solid. Several numerical examples are also presented to demonstrate that the proposed immersed continuum method is a good candidate for multi-scale and multi-physics modeling platform.

G501 Immersed Finite Element Methodによる流体-剛体連成解析(2)(GS-5 数値シミュレーション,一般セッション)

IFEM (Immersed Finite Element Method) is an extended method from Immersed Boundary Method which is familiar as Finite Difference Method. In IFEM, the motion of structure is described as Lagrangian while that of fluid as Eulerian, and then the fluidstructure interaction force is added to the equations of motion for fluid using Dirac delta function. Therefore the reproduction of fluid meshes is not necessary. In the present paper, the conventional IFEM that is frequently utilized for fluid and flexible elastic structure interaction problems is applied to fluid-rigid bodies system by introducing the simple evaluation of internal force as zero and the reassignment of average velocity to rigid body.

An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction

Arbitrary Lagrangian–Eulerian (ALE) techniques provide a general framework for solving moving boundary flows and fluid–structure interaction problems. ALE formulations allow freedom of prescribing the fluid mesh velocity which can be independent of the velocity of the fluid particles. A major challenge in ALE descriptions lies in developing mesh moving techniques to update the fluid mesh and map the moving domain in a rational way. Exploiting the notion of arbitrary mesh velocity for the fluid domain, we have developed an adaptive mesh rezoning technique for structured and unstructured meshes. The method has been applied to meshes composed of triangles, quadrilaterals, as well as an arbitrary combination of these two element types in the computational domain. This feature of the proposed scheme is very attractive from practical problem solving viewpoint in that it allows kinematically complex problems to be handled effectively. A variety of test cases are shown that involve single and/or multiple moving objects. Embedding the mesh rezoning scheme in our flow solver, we also present some representative simulations of flows over moving meshes.

Computation of flow problems with the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT)

In computation of flow problems with fluid–solid interfaces, an interface-tracking technique, where the fluid mesh moves to track the interface, would allow us to have full control of the resolution of the fluid mesh in the boundary layers. With an interface-capturing technique (or an interface locator technique in the more general case), on the other hand, independent of how accurately the interface geometry is represented, the resolution of the fluid mesh in the boundary layer will be limited by the resolution of the fluid mesh at the interface. In computation of flow problems with fluid–fluid interfaces where the interface is too complex or unsteady to track while keeping the remeshing frequency under control, interface-capturing techniques, with enhanced-discretization as needed, could be used as more flexible alternatives. Sometimes we may need to solve flow problems with both fluid–solid interfaces and complex or unsteady fluid–fluid interfaces. The Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) was introduced for computation of flow problems that involve both interfaces that can be accurately tracked with a moving mesh method and interfaces that are too complex or unsteady to be tracked and therefore require an interface-capturing technique. As the interface-tracking technique, we use the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation. The interface-capturing technique rides on this, and is based on solving over a moving mesh, in addition to the Navier–Stokes equations, the advection equation governing the time-evolution of the interface function. For the computations reported in this paper, as interface-capturing technique we are using one of the versions of the Edge-Tracked Interface Locator Technique (ETILT).

A three-dimensional fluid–structure interaction method for heart valve modelling

A method is presented for modelling fluid–solid interaction with large transformations of a slender solid body. The fluid flow is described by the unsteady Navier–Stokes equation, and the solid deformation is described by an incompressible hyperelastic Neo-Hookean model. Although the fluid and solid mesh are non-conformal with respect to each other, both domains can be coupled using a Lagrange multiplier. Accuracy and robustness are improved by a computationally inexpensive adaptive meshing scheme which is applied to the fluid mesh at the position of the solid interface. To illustrate the applicability of this method, 2D and 3D model problems are presented that are closely related to dynamical heart-valve computations. To cite this article: R. van Loon et al., C. R. Mecanique 333 (2005).

Immersed finite element method and its applications to biological systems

This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid–structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid sub-domains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid–structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility.

Development of a New Interfacing Strategy for Fluid-Structure Interaction

Displacement and pressure transfer between fluid and structure meshes in fluidstructure interaction analysis is complicated substantially when the two meshes on the domain interface are different and therefore form two distinct surfaces in three-dimensional space. A new, approximately energy-conserving interfacing strategy with two distinct components - mapping and interpolation - is proposed. The mapping between meshes is based on the assumption of a common parametric-based description of the wetted surface. The interpolation strategy is based on the smoothing element analysis method developed to recover stresses in finite element analysis, with an additional term to impose an energy-conserving constraint. The method is evaluated numerically with several examples from linear hydrodynamics/hydroelasticity. The advantage of these examples is that the components can be evaluated separately, and the performance of the method can be examined more clearly. Numerical results show the method is quite promising.

The ping‐pong cannon demonstration: Optical studies and numerical simulation

This presentation describes the use of laser pulse photography, optical timing, pulsed Schlieren, and heterodyne interferometry to look more closely at the fluid dynamics of a recently popular lecture demonstration—the so‐called ‘‘ping‐pong cannon.’’ Optical diagnostic techniques have been applied to two types of these cannons, and led to greater knowledge of the kinematics of the accelerating ball, along with some insight into the exit mechanism and subsequent target interactions. Also will be described how a 1D numerical simulation allows visualization of shock wave formation within the tube during ball acceleration. Solutions of the Euler equation are obtained using the method of space‐time finite elements, while the ball is tracked as an interface in the compressible fluid mesh. [Work supported in part by the MN NASA Space Grant and the Carlsen‐Lewis Endowment of Bethel University.]

Free surface tracking for the accurate time response analysis of nonlinear liquid sloshing

Liquid sloshing displays the highly nonlinear free surface fluctuation when either the external excitation is of large amplitude or its frequency approaches natural sloshing frequencies. Naturally, the accurate tracking of time-varying free surface configuration becomes a key task for the reliable prediction of the sloshing time-history response. However, the numerical instability and dissipation may occur in the nonlinear sloshing analysis, particularly in the longtime beating simulation, when two simulation parameters, the relative time-increment parameter a and the fluid mesh pattern, are not elaborately chosen. This paper intends to examine the effects of these two parameters on the potential-based nonlinear finite element method introduced for the large amplitude sloshing flow.

Multibladerow Forced Response Modeling in Axial-Flow Core Compressors

This paper describes the formulation and application of an advanced numerical model for the simulation of blade-passing and low-engine order forced response in turbomachinery core compressors. The Reynolds averaged Navier–Stokes equations are used to represent the flow in a nonlinear time-accurate fashion on unstructured meshes of mixed elements. The structural model is based on a standard finite-element representation. The fluid mesh is moved at each time step according to the structural motion so that changes in blade aerodynamic damping and flow unsteadiness can be accommodated automatically. A whole-annulus 5-bladerow forced response calculation, where three upstream and one downstream bladerows were considered in addition to the rotor bladerow of interest, was undertaken using over 20 million grid points. The results showed not only some potential shortcomings of equivalent 2-bladerow computations for the determination of the main blade-passing forced response, but also revealed the potential importance of low engine-order harmonics. Such harmonics, due to stator blade number differences, or arising from common symmetric sectors, can only be taken into account by including all stator bladerows of interest. The low engine-order excitation that could arise from a blocked passage was investigated next. It was shown that high vibration response could arise in such cases.

Whole-annulus aeroelasticity analysis of a 17-bladerow WRF compressor using an unstructured Navier–Stokes solver

This paper describes a large-scale aeroelasticity computation for an aero-engine core compressor. The computational domain includes all 17 bladerows, resulting in a mesh with over 68 million points. The Favre-averaged Navier–Stokes equations are used to represent the flow in a non-linear time-accurate fashion on unstructured meshes of mixed elements. The structural model of the first two rotor bladerows is based on a standard finite element representation. The fluid mesh is moved at each time step according to the structural motion so that changes in blade aerodynamic damping and flow unsteadiness can be accommodated automatically. An efficient domain decomposition technique, where special care was taken to balance the memory requirement across processors, was developed as part of the work. The calculation was conducted in parallel mode on 128 CPUs of an SGI Origin 3000. Ten vibration cycles were obtained using over 2.2 CPU years, though the elapsed time was a week only. Steady-state flow measurements and predictions were found to be in good agreement. A comparison of the averaged unsteady flow and the steady-state flow revealed some discrepancies. It was concluded that, in due course, the methodology would be adopted by industry to perform routine numerical simulations of the unsteady flow through entire compressor assemblies with vibrating blades not only to minimise engine and rig tests but also to improve performance predictions.

Initialisation of volume fraction in fluid/structure interaction problem

In this paper, an algorithm that generates volume fraction initialisation for fluid-structure interaction problems is presented and implemented in an Arbitrary Lagrangian Eulerian (ALE) code. This algorithm improves the flexibility and efficiency of multi-material ALE formulations, enabling fluid-structure coupling problems to be dealt with, in which complex-shaped structures are embedded in a Cartesian fluid mesh, and where several fluid materials are involved. When implemented in a finite element code the algorithm will be extremely useful in the modelling of highly transient problems involving fluid-structure interactions and complex structural topologies. In such problems the volume fraction of each cell must be accurately initialised in order for the fluid-structure coupling algorithm to be effective. In many fluid-structure coupling problems if the volume fraction initialisation is not processed properly, the coupling algorithm leads to numerical fluid leakage through the structure involving an erroneous solution. In this paper the volume fraction initialisation method is described in detail and applied to the modelling of a cylindrical shock tube problem and to a crash problem involving a fuel tank of complex geometry under braking conditions.

Development of Strong Coupling Method Considering Non-conforming Mesh on Fluid-Structure Interface (1st Report, Verification of Method)

This paper describes a strong coupling method considering non-conforming mesh on fluid-structure interface. In the present method, a transformation matrix derived from the geometrical relations between non-conforming fluid and structural meshes on fluid-structure interface is directly combined with the formulation of the strong coupling method to satisfy the compatibility and equilibirium conditions on fluid-structure interface. The conjugate gradient method is applied to solve the derived coupled equation system by introducing the consistent pressure Poisson equation. To verify basic characteristics of the proposed method, it is applied for free vibration of a cylinder in quiescent fluid. The added mass and damping coefficients derived by the present method agree well with those by other researchers.

A combined fictitious domain/adaptive meshing method for fluid–structure interaction in heart valves

AbstractA new approach for modelling the fluid‐structure interaction of flexible heart valves is proposed. Using a finite element method, a Lagrangian description of a non‐linear solid and an Eulerian description of a fluid are coupled by a Lagrange multiplier. This multiplier allows the solid and fluid mesh to be non‐conform. Solid displacements and fluid velocities are described well in such a fictitious domain approach. However, the accuracy of pressures and shear stresses in the vicinity of the solid are poor. Therefore an inexpensive mesh‐adaptation algorithm is applied, which adapts the fluid mesh to the position of the solid mesh every time step. This minor adjustment of the fluid mesh makes it possible to sustain a physiological pressure gradient across a solid leaflet. Furthermore, shear stresses can be computed at both sides of the leaflet. The method is demonstrated for a 2D example, however with a scope to 3D modelling. Copyright © 2004 John Wiley & Sons, Ltd.

FINITE ELEMENT ANALYSIS OF NON-LINEAR FLUID STRUCTURE INTERACTION IN HYDRODYNAMICS USING MIXED LAGRANGIAN-EULERIAN METHOD

Fluid structure Interaction (FSI) is important in analysis of: (1) Cardio-vascular dynamics; (2) Underwater/ Offshore structures; (3) Aircraft wings and turbine blade designs; (4) Design of tall structures/buildings; (5) high speed hard disk drives etc. At present, such capabilities are being incorporated, if any, only to a limited extent in commercial CFD codes leaving the engineers to develop their own codes. In the current study, a hydro-elastic problem of an underwater structure has been considered. Traditionally, the hydrodynamics and the structural dynamics are solved using finite difference/boundary element methods and finite element method (FEM) respectively. Moreover, the governing equation for fluid and structure are usually written in Eulerian and Lagrangian reference frames - posing further difficulties for coupling the two systems. In this research, both the fluid and structural systems are solved by the finite element method using a mixed Eulerian-Lagrangian scheme, where, fluid mesh moves and adapts to new free surface and structural positions. A full non-linear free surface implementation is considered. A mesh adaptation using Laplacian smoothing is performed to reduce the need for re-meshing the domain frequently. The scheme is validated with solutions available in the literature and extended to the present FSI problem with non-linear free surface boundary condition.

A monolithic approach to fluid–structure interaction using space–time finite elements

The paper presents a simultaneous solution procedure for fluid–structure interaction problems. The structural motion is described by geometrically nonlinear elastodynamics. The fluid is modeled by the incompressible Navier–Stokes equations. The space–time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure. In order to enforce momentum conservation and geometric continuity at the interface, a weighted residual formulation of coupling conditions is introduced. The discretized model equations for fluid, structure and coupling conditions are formulated in a single equation system. The nonlinear system and the fluid mesh movement are solved in a single iteration loop. Two-dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology.

A comparative study of dynamic mesh updating methods used in the simulation of fluid-structure interaction problems with a non-linear free surface

This paper compares the performance of three mesh movement algorithms: Laplacian smoothing, linear spring analogy and torsion spring analogy for a fluid mesh update in staggered fluid-structure interaction (FSI) simulations with a non-linear free surface. The mesh updating schemes are applied to simulate three representative cases of the above-stated dual moving boundary problem. The performances of the algorithms are gauged on the basis of their ability to delay the initiation of a complete remesh of the fluid domain while maintaining solution accuracy. To satisfy this dual objective, the mesh-updating algorithm should not only prevent mesh failure but should also maintain well-shaped triangles. The reasons for the failure of different schemes are explained and suitable modifications are suggested/implemented to enhance thier performance. It is shown that these modifications prove to be very successful in improving the effectiveness of the algorithms.

Enhanced-discretization space–time technique (EDSTT)

The enhanced-discretization space–time technique (EDSTT) was developed for the purpose of being able to, in the context of a space–time formulation, enhance the time-discretization in regions of the fluid domain requiring smaller time steps. Such requirements are often encountered in time-accurate computations of fluid–structure interactions, where the time-step size required by the structural dynamics part is smaller, and carrying out the entire computation with that time-step size would be too inefficient for the fluid dynamics part. In the EDSTT-single-mesh (EDSTT-SM) approach, a single space–time mesh, unstructured both in space and time, would be used to enhance the time-discretization in regions requiring smaller time steps. In the EDSTT-multi-mesh (EDSTT-MM) approach, we complement the space–time concept of the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation with the multi-mesh concept of the enhanced-discretization interface-capturing technique (EDICT). In applications to fluid–structure interactions, the structural dynamics modeling is based on a single space–time mesh and the fluid dynamics modeling is based on two space–time meshes. The structural dynamics interface nodes in the space–time domain also belong to the second fluid mesh, which accommodates the time-step requirement of the structural dynamics. We apply the EDSTT-SM and EDSTT-MM approaches to a number of test problems to demonstrate how these methods work and why they would be desirable to use in time-accurate computations.