Fluid–structure interaction simulation of aortic blood flow

The numerical tools to simulate blood flow in the cardiovascular system are constantly developing due to the great clinical interest and to scientific advances in mathematical models and computational power. The present work aims to address and validate new algorithms to efficiently predict the hemodynamics in large arteries. These algorithms rely on finite elements simulation of the fluid–structure interaction between blood flow and arterial wall deformation of a healthy aorta. Different sets of boundary conditions are devised and tested. The mean velocity and pressure time evolution is plotted on different sections of the aorta and the wall shear stress distribution is computed. The results are compared with those obtained with a rigid wall simulation. Pulse wave velocity is computed and compared with the values available from the literature. The flow boundary conditions used for the outlets are obtained using the solution of a one-dimensional model. The results of the simulations are in agreement with the physiological data in terms of wall shear stress, wall displacement, pressure waveforms and velocities.     

Three-dimensional free surface simulation

A 3D boundary element method with linear triangular element has been developed for the simulation of the free surface subjected to the surface tension force. A liquid droplet and a liquid jet are chosen to be the studying cases for the free surface simulation. The codes include 3D Laplace's solver, grid generation, and free surface module for the calculation of surface normal vector, surface curvature, and tangential velocity. Distortion of a droplet has shown the corresponding mode oscillation by specifying a given order of Legendre function for the initial velocity potential. And, the comparison of computational results and the predicted values from the dispersion equation, which serves as the analytical solution for the growth rate, for the temporal instability analysis on a liquid jet shows a very good agreement. This has shown that the proposed model is capable of the complex 3D liquid jet simulation.     

Numerical simulation of interaction between turbulent flow and a vibrating airfoil

The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element treatment of the Reynolds averaged Navier–Stokes (RANS) approach, the use of turbulence models and the solution of the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers up to 10⁶ require to use a suitable stabilization of the finite element discretization and the application of a turbulence model. We apply the algebraic turbulence model, which was designed by Baldwin and Lomax and modified by Rostand. The developed technique was tested by the simulation of flow past a flat rigid plate and the computation of pressure distribution around a rotating airfoil with prescribed motion. Finally, the method was applied to the simulation of flow induced airfoil vibrations. This research was supported under the Grant No. IAA200760613 of the Grant Agency of Academy of Sciences of the Czech Republic. The research of M. Feistauer was partly supported by the research project MSM 0021620839 financed by the Ministry of Education of the Czech Republic and the research of L. Dubcová was partly supported by the grant No. 48607 of the Grant Agency of the Charles University. The authors acknowledge the support of these institutions.     

Application of lattice Boltzmann method in free surface flow simulation of micro injection molding

The filling flow in micro injection molding was simulated by using the lattice Boltzmann method (LBM). A tracking algorithm for free surface to handle the complex interaction between gas and liquid phases in LBM was used for the free surface advancement. The temperature field in the filling flow is also analyzed by combining the thermal lattice Boltzmann model and the free surface method. To simulate the fluid flow of polymer melt with a high Prandtl number and high viscosity, a modified lattice Boltzmann scheme was adopted by introducing a free parameter in the thermal diffusion equation to overcome the restriction of the thermal relaxation time. The filling flow simulation of micro injection molding was successfully performed in the study.     

Numerical simulation of 3D fluid–structure interaction flow using an immersed object method with overlapping grids

The newly developed immersed object method (IOM) [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids. J Comput Phys 2005; 207(1): 151–72] is extended for 3D unsteady flow simulation with fluid–structure interaction (FSI), which is made possible by combining it with a parallel unstructured multigrid Navier–Stokes solver using a matrix-free implicit dual time stepping and finite volume method [Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method. In: The second M.I.T. conference on computational fluid and solid mechanics, June 17–20, MIT, Cambridge, MA 02139, USA, 2003; Tai CH, Zhao Y, Liew KM. Parallel computation of unsteady three-dimensional incompressible viscous flow using an unstructured multigrid method, Special issue on “Preconditioning methods: algorithms, applications and software environments. Comput Struct 2004; 82(28): 2425–36]. This uniquely combined method is then employed to perform detailed study of 3D unsteady flows with complex FSI. In the IOM, a body force term F is introduced into the momentum equations during the artificial compressibility (AC) sub-iterations so that a desired velocity distribution V₀ can be obtained on and within the object boundary, which needs not coincide with the grid, by adopting the direct forcing method. An object mesh is immersed into the flow domain to define the boundary of the object. The advantage of this is that bodies of almost arbitrary shapes can be added without grid restructuring, a procedure which is often time-consuming and computationally expensive. It has enabled us to perform complex and detailed 3D unsteady blood flow and blood–leaflets interaction in a mechanical heart valve (MHV) under physiological conditions.     

Numerical simulation of two-phase free surface flows

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a two-grids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized.     

Numerical simulation of the fluid–structure interaction between air blast waves and free-standing plates

A numerical method is used to compute the flow field corresponding to blast waves of different incident profiles propagating in air and impinging on free-standing plates. The method is suitable for the consideration of compressibility effects in the fluid and their influence on the plate dynamics. The history of the pressure experienced by the plate is extracted from numerical simulations for arbitrary blast strengths and plate masses and used to infer the impulse per unit area transmitted to the plate. The numerical results complement some recent analytical solutions in the intermediate range of plate masses and arbitrary blast intensities where exact solutions are not available. The resulting beneficial effect of the fluid–structure interaction (FSI) in reducing transmitted impulse in the presence of compressibility effects is discussed. In particular, it is shown that in order to take advantage of the impulse reduction provided by the FSI effect, large plate displacements are required which, in effect, may limit the practical applicability of exploiting FSI effects in the design of blast-mitigating systems.     

A numerical method for the simulation of free surface flows with surface tension

A numerical model for the simulation of three-dimensional liquid–gas flows with free surfaces and surface tension is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface.

An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquid–gas interface, the method described in [Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 2005;203(2):626–49] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh.

The model is validated and numerical results in two and three space dimensions are presented for bubbles and/or droplets flows.     

Improving the efficiency of a Godunov-based free surface flow model

Models for simulating turbulent, nonhydrostatic, free surface flow are highly complex and require the combination of several different physical phenomena. Consequently, there are many different approaches to design such a model. This paper explores ways to improve the numerical efficiency of an existing free surface flow model without severely sacrificing its accuracy. Specifically, this paper investigates alternative methods for integrating diffusion as well as extending the model to nonhydrostatic flow.     

Numerical simulation of free surface flows on a fish bypass

A computational fluid dynamics (CFD) model is developed to better understand the complex flow field inside a free surface fish bypass constructed at Rocky Reach Dam. This facility consists of two identical parallel channels, with fish screens on the side walls of each channel, and a pump station recirculating 96% of incoming flows into the forebay. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations, with a standard κ-ε turbulence model. The volume of fluid (VOF) method is used to predict free surface elevations. A proportional controller is implemented in the model to achieve a target flow rate at the pump exits. The pressure drop in the fish screens is modeled using porous media. Quantitative validation and visualization of the flow field characteristics indicate that CFD modeling may be a useful tool for fish passage design.     

Numerical simulation of fluid–structure interaction by SPH

A Lagrangian model for the numerical simulation of fluid–structure interaction problems is proposed in the present paper. In the method both fluid and solid phases are described by smoothing particle hydrodynamics: fluid dynamics is studied in the inviscid approximation, while solid dynamics is simulated through an incremental hypoelastic relation. The interface condition between fluid and solid is enforced by a suitable term, obtained by an approximate SPH evaluation of a surface integral of fluid pressure.The method is validated by comparing numerical results with laboratory experiments where an elastic plate is deformed under the effect of a rapidly varying fluid flow.     

The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell

A mathematical model for describing the interaction between a compressible fluid and an elastic shell is formulated as an initial boundary value problem. The partial differential equations of the model are discretized both in time and space by a finite-difference method. The stability of the resulting explicit difference schemes is analyzed by Kreiss' theory for the stability analysis of difference schemes in initial boundary value problems. It is shown that the stability properties of the schemes for the interaction problem may be influenced by the type of discretization in space used for the contact condition on the interface between the fluid and the shell and also by the approximation of the hydrodynamic pressure on the surface of the shell. A simple sufficient condition is found that will ensure the best possible stability properties of the schemes. Several of these, which are of practical interest, are analyzed.     

Variable domain finite element analysis of free surface gravity flow

A variable domain finite element method is presented for the solution of problems in gravity flow with free surfaces. Novel features of the method are the use of a functional with a variable domain of integration and a finite element mesh that can adapt automatically to all compatible variations in the domain. The finite element solution gives the streamlines and the flow rate associated with any stagnation level and system geometry. The method is applied to flow over spillway and gives results that agree extremely well with experimental data.     

硫醇类硫化物与H+相互作用的分子模拟

为了研究催化裂化、加氢等工艺过程中,硫醇类硫化物与固体酸性催化剂的B酸中心之间的相互作用机理,采用动力学和半经验量子力学方法,对几种典型硫醇类硫化物与H+之间的相互作用进行了研究.以2-戊硫醇、环己硫醇和硫酚为模型化合物,模拟计算了各硫醇类硫化物的最高占据轨道(HOMO)以及H+进攻硫位及不同碳位时所形成中间体的生成热及键长变化,进而讨论H+的优先进攻位置以及反应中间体的稳定性.结果表明,H+的进攻位置对形成的中间体的稳定性有很大影响.当H+进攻硫醇类硫化物中的碳位时,反应中间体的生成热远大于或接近于H+直接进攻硫位所形成的中间体的生成热;对于反应中间体的生成热同进攻硫位所形成的中间体的生成热相近的碳原子上的质子化反应,其实质与直接进攻硫原子时相一致,并生成硫化氢,这说明H+将优先进攻硫醇类硫化物中的硫原子.由此可以认为,硫醇类硫化物在固体酸性催化剂的作用下,由于B酸中心的给质子性质,较容易在硫位上发生质子化反应,以生成硫化氢的形式转化脱除.     

Optimization and stabilization of LBM free surface flow simulations using adaptive parameterization

We present a method to speed up and stabilize free surface simulations with the lattice Boltzmann method (LBM). This is done by adaptively changing the parameterization of the simulation in a way that corresponds to a different size of the simulation time step. This means that the Mach number changes as well, and requires a rescaling of all distribution functions. Hence we only perform the rescaling when the velocities in the simulation become too large or small. We will demonstrate the effect of this procedure for two and three-dimensional test cases. In addition to a reduction of the necessary LBM steps, this method can also be used to stabilize gravity driven simulations, where the maximum velocities are not known a priori.     

Transient simulation of friction-induced vibrations using an elastic multibody approach

In this paper, by the use of elastic multibody dynamics and a master–slave contact approach with penalty formulation, computationally efficient time integrations of a brake system are performed for constant and time-dependent input parameters. As a result, the amplitudes of the friction-induced vibrations and the contact forces at the disc–pad interfaces are predicted. Besides, system outputs are viewed in phase diagrams, and the creation of a stable limit cycle for a low friction coefficient is identified. In this way, conclusions on the stability of the system are drawn, and statements based on frequency-domain analyses are complemented. Finally, a distinct need for a new criterion that quantifies the squeal propensity of such systems in the time domain is identified.     

A component-based parallel infrastructure for the simulation of fluid–structure interaction

The Uintah computational framework is a component-based infrastructure, designed for highly parallel simulations of complex fluid–structure interaction problems. Uintah utilizes an abstract representation of parallel computation and communication to express data dependencies between multiple physics components. These features allow parallelism to be integrated between multiple components while maintaining overall scalability. Uintah provides mechanisms for load-balancing, data communication, data I/O, and checkpoint/restart. The underlying infrastructure is designed to accommodate a range of PDE solution methods. The primary techniques described here, are the material point method (MPM) for structural mechanics and a multi-material fluid mechanics capability. MPM employs a particle-based representation of solid materials that interact through a semi-structured background grid. We describe a scalable infrastructure for problems with large deformation, high strain rates, and complex material behavior. Uintah is a product of the University of Utah Center for Accidental Fires and Explosions (C-SAFE), a DOE-funded Center of Excellence. This approach has been used to simulate numerous complex problems, including the response of energetic devices subject to harsh environments such as hydrocarbon pool fires. This scenario involves a wide range of length and time scales including a relatively slow heating phase punctuated by pressurization and rupture of the device.     

N-body modeling of nonlinear,free surface liquid flow

In this paper a new, n-body approach is developed for the modeling of liquid phenomena. Both long and short range forces are included. Computer examples of several prototype, nonlinear, free surface problems are described and discussed.     

Transitional cylindrical swirling flow in presence of a flat free surface

This article is devoted to the study of an incompressible viscous flow of a fluid partly enclosed in a cylindrical container with an open top surface and driven by the constant rotation of the bottom wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry and of the prescribed boundary conditions of Dirichlet type—no-slip on the cavity walls. The top surface of the cylindrical cavity is left open with an imposed stress-free boundary condition, while a no-slip condition with a prescribed rotational velocity is imposed on the bottom wall. The Reynolds regime corresponds to transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new flow states that were investigated based on a fully three-dimensional solution of the Navier-Stokes equations for the free-surface cylindrical swirling flow, without resorting to any symmetry property unlike all other results available in the literature. Theses solutions are obtained through direct numerical simulations based on a Legendre spectral element method.     

Hybrid LES/RANS modelling of free surface flow through vegetation

Vegetated channels are environmentally friendly and frequently used to convey water for drainage and recreational purposes. The design and assessment of these channels often requires the use of numerical models which are based on the Reynolds Averaged Navier-Stokes (RANS) approach or Large Eddy Simulations (LES). It is well accepted that both approaches have their advantages and disadvantages. To overcome these disadvantages a hybrid model combining the RANS and LES methodologies is proposed in this work. The major task for the model development is to couple the RANS and the LES models effectively. Various methods have been investigated and the results are as follows. At the inflow boundary of the computational domain, a semi-analytical velocity profile for submerged vegetation is used as the RANS inflow condition to shorten the unrealistic flow transition region. At the interface of the upstream RANS region and the downstream LES region, turbulence fluctuations are artificially generated using a spectral line processor, with the mean velocity determined by using the frozen cloud assumption. At the interface of the upstream LES region and the downstream RANS region, a virtual momentum sink is imposed to dissipate the sub-grid scale fluctuations and to shorten the transition region. The final model has been verified against experiments of flow through submerged and emergent vegetation, as well as a partly vegetated channel.