A unified operator splitting approach for multi-scale fluid–particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for the coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.     

Large and Small Eddies Matter: Animating Trees in Wind Using Coarse Fluid Simulation and Synthetic Turbulence

Animating trees in wind has long been a problem in computer graphics. Progress on this problem is important for both visual effects in films and forestry biomechanics. More generally, progress on tree motion in wind may inform future work on two‐way coupling between turbulent flows and deformable objects. Synthetic turbulence added to a coarse fluid simulation produces convincing animations of turbulent flows but two‐way coupling between the enriched flow and objects embedded in the flow has not been investigated. Prior work on two‐way coupling between fluid and deformable models lacks a subgrid resolution turbulence model. We produce realistic animations of tree motion by including motion due to both large and small eddies using synthetic subgrid turbulence and porous proxy geometry. Synthetic turbulence at the subgrid scale is modulated using turbulent kinetic energy (TKE). Adding noise after sampling the mean flow and TKE transfers energy from small eddies directly to the tree geometry. The resulting animations include both global sheltering effects and small scale leaf and branch motion. Viewers, on average, found animations, which included both coarse fluid simulation and TKE‐modulated noise to be more accurate than animations generated using coarse fluid simulation or noise alone.     

Realistic Animation of Fluid with Splash and Foam

In this paper we describe a method for modeling and rendering dynamic behavior of fluids withsplashes and foam. A particle system is built into a fluid simulation system to represent an ocean wavecresting and spraying over another object. We use the Cubic Interpolated Propagation (CIP) method asthe fluid solver. The CIP method can solve liquid and gas together in the framework of fluid dynamicsand has high accuracy in the case of relatively coarse grids. This enables us to simulate the fluids in ashort time and describe the motion of splashes in the air that is associated with the liquid motion well.The foam floating on the water also can be described using the particle system. We integrate the rigidbody simulation with the fluid and particle system to create sophisticated scenes including splashes andfoam. We construct state change rules that are used with the particle system. This controls the generation,vanishing and transition rule of splashes and foam. The transition rule makes the seamless connection betweena splash and foam. We employed a fast volume rendering method with scattering effect for particles.One of the important features of our method is the combination of fast simulation and rendering techniques,which provides dynamic and realistic scenes in a short time.     

Wake Synthesis For Shallow Water Equation

In fluid animation, wake is one of the most important phenomena usually seen when an object is moving relative to the flow. However, in current shallow water simulation for interactive applications, this effect is greatly smeared out. In this paper, we present a method to efficiently synthesize these wakes. We adopt a generalized SPH method for shallow water simulation and two way solid fluid coupling. In addition, a 2D discrete vortex method is used to capture the detailed wake motions behind an obstacle, enriching the motion of SWE simulation. Our method is highly efficient since only 2D simulation is required. Moreover, by using a physically inspired procedural approach for particle seeding, DVM particles are only created in the wake region. Therefore, very few particles are required while still generating realistic wake patterns. When coupled with SWE, we show that these patterns can be seen using our method with marginal overhead.     

利用弹簧质点模型和隐式方法的布料模拟研究

首先运用弹簧-质点模型建立布料的面模型,然后对质点进行力的分解以及受力分析并优化。提出逼近的隐式数值积分方法模拟质点的运动轨迹,这解决了显式数值积分方法的不稳定性和小时间间隔的缺点和其他隐式方法计算量大的缺点,这也是实现基于物理模型的布料仿真的关键技术。针对具体碰撞对象采用简单的包围盒方法进行碰撞检测,和利用二分法进行碰撞的处理,大大增加了碰撞处理的逼真效果。实验证明其模拟方法具有稳定性和实用性。     

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.     

Particle‐based realistic simulation of fluid–solid interaction

In this paper a novel method for simulating incompressible viscous fluid and solid coupling is presented. In the coupling model, a rigid object is treated as a special fluid constrained to rigid body motion. To animate the coupling model, the Smoothed Particle Hydrodynamics method is used for solving the fluid motion equations. For keeping the rigidity of rigid objects, the total force and total torque exerted on solids is first worked out according to the impulse–momentum theorem, and then the movement of these rigid bodies is restricted to translations and rotations. Moreover, in order to prevent the fluids particles leaking into solids, a detection and correction procedure is presented, and the velocities of fluid particles will be tuned if the penetration is detected in this procedure. The proposed method can be implemented easily by extending the existing fluid solvers, the experimental results show that this method is capable of animating the realistic solid and fluid coupling. Copyright © 2010 John Wiley & Sons, Ltd.     

Non-coaxial rotating flow of viscous fluid with heat and mass transfer

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.

     

Double-diffusive and Soret-induced convection of a micropolar fluid in a vertical channel

This paper reports an investigation of the fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel. Asymmetric temperature and concentration boundary conditions are applied to the walls of the channel. The cases of double diffusion and Soret-induced convection are both considered. The governing parameters for the problem are the buoyancy ratio and the various material parameters of the micropolar fluid. The resulting non-dimensional boundary value problem is solved analytically in closed form using MAPLE software. A numerical solution of the time dependent governing equations is demonstrated to be in good agreement with the analytical model. The influence of the governing parameters on the fluid flow as well as heat and solute transfers is demonstrated to be significant.     

Natural frequencies of tube bundle in an uncompressible fluid

A method of eigenfrequency computation for a cluster of tubes immersed in an uncompressible liquid is described. Several numerical examples are presented, showing that the presence of fluid involves the spreading of the natural frequencies of the tubes in vacuum. A lower bound of these eigenfrequencies can be obtained for a spatially periodic bundle.     

热膨胀过程中流固耦合应力分析的等效方法

密闭容器内的液体受热膨胀后,会挤压容器并使其受力变形直至破裂,而传统的流固耦合分析方法难以解决这种流固耦合场、应力场和温度场等多场耦合的问题.利用等效表面载荷的方法来模拟膨胀的液体与固体之间的相互作用,可分析在温度升高过程中内部充满液体的某个容器的受力情况.通过本方法对容器进行动态应力分析,可等效得到容器某个部分结构失效时,容器内壁所受载荷的具体大小及其容积的变化,并可对应得到某处结构失效时刻的准确温度.该方法可有效解决多场耦合的问题,并且省去液体模型,提高分析和计算速度.结合电池冷却箱受热膨胀的算例进一步阐释该方法.     

The Lattice-boltzmann method for simulating gaseous phenomena

We present a physically-based, yet fast and simple method to simulate gaseous phenomena. In our approach, the incompressible Navier-Stokes (NS) equations governing fluid motion have been modeled in a novel way to achieve a realistic animation. We introduce the lattice Boltzmann model (LBM), which simulates the microscopic movement of fluid particles by linear and local rules on a grid of cells so that the macroscopic averaged properties obey the desired NS equations. The LBM is defined on a 2D or 3D discrete lattice, which is used to solve fluid animation based on different boundary conditions. The LBM simulation generates, in real-time, an accurate velocity field and can incorporate an optional temperature field to account for the buoyancy force of hot gas. Because of the linear and regular operations in each local cell of the LBM grid, we implement the computation in commodity texture hardware, further improving the simulation speed. Finally, textured splats are used to add small scale turbulent details, achieving high-quality real-time rendering. Our method can also simulate the physically correct action of stationary or mobile obstacles on gaseous phenomena in real-time, while still maintaining highly plausible visual details.     

Planar array of corrugated tapered slot antennas for ultrawideband biomedical microwave imaging system

A planar antenna array that includes 12 corrugated tapered slot elements for use in ultrawideband (UWB) biomedical microwave imaging systems is presented. The used corrugate tapered slot antenna has a compact size, low profile, moderate gain, and distortionless performance in the time domain. The array is immersed in a carefully designed matching liquid of suitable dielectric constant to improve the matching between the array and the imaged object, and thus, to increase the dynamic range of the imaging system. A suitable platform is designed and fabricated to accommodate the array, breast phantom, and a coupling liquid for the case of UWB breast imaging. The design of the whole system is optimized using trust‐region framework method in the simulation tool CST Microwave Studio. The performance of the designed array is confirmed via measurements in a realistic imaging environment. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Eigenfrequencies of a tube bundle placed in a confined fluid

The problem of natural vibration of a group of immersed tubes is investigated, and it is shown that the presence of the fluid has the effect of spreading the mechanical resonance frequencies of the tubes over intervals of varying width, and of introducing eigenfrequencies between these ranges. The case of compressible or uncompressible fluid is examined. Several computation methods are described.     

基于牛顿-欧拉方程的固流耦合模拟

依据牛顿-欧拉方程,结合力矩和表面张力理论,设计了一组新的基于网格的水波-物体交互方程,模拟了由点波源引起的水波运动,以及水和固体共同存在时,二者之间的相互作用影响各自的运动状态。详细分析了在这种固流耦合情况中,水波遇到障碍物引起的波纹的变化,以及物体在网格力和转动力的作用下,运动状态随位置、能量和时间改变的变化规律,其中还考虑了表面张力对物体运动状态的影响。从实验效果图看,水波和物体的运动都较为自然真实。     

Boundary Handling at Cloth–Fluid Contact

We present a robust and efficient method for the two‐way coupling between particle‐based fluid simulations and infinitesimally thin solids represented by triangular meshes. Our approach is based on a hybrid method that combines a repulsion force approach with a continuous intersection handling to guarantee that no penetration occurs. Moreover, boundary conditions for the tangential component of the fluid's velocity are implemented to model the different slip conditions. The proposed method is particularly useful for dynamic surfaces, like cloth and thin shells. In addition, we demonstrate how standard fluid surface reconstruction algorithms can be modified to prevent the calculated surface from intersecting close objects. For both the two‐way coupling and the surface reconstruction, we take into account that the fluid can wet the cloth. We have implemented our approach for the bidirectional interaction between liquid simulations based on Smoothed Particle Hydrodynamics (SPH) and standard mesh‐based cloth simulation systems.     

On the computational power of circuits of spiking neurons

Complex real-time computations on multi-modal time-varying input streams are carried out by generic cortical microcircuits. Obstacles for the development of adequate theoretical models that could explain the seemingly universal power of cortical microcircuits for real-time computing are the complexity and diversity of their computational units (neurons and synapses), as well as the traditional emphasis on offline computing in almost all theoretical approaches towards neural computation. In this article, we initiate a rigorous mathematical analysis of the real-time computing capabilities of a new generation of models for neural computation, liquid state machines, that can be implemented with—in fact benefit from—diverse computational units. Hence, realistic models for cortical microcircuits represent special instances of such liquid state machines, without any need to simplify or homogenize their diverse computational units. We present proofs of two theorems about the potential computational power of such models for real-time computing, both on analog input streams and for spike trains as inputs.     

Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method

General formulae are derived to calculate the hydrodynamic force acting on a solid object, either stationary or in motion, when an immersed boundary (IB) method is used to simulate the flow around the object. These formulae explore the fact that the imposed force term in the IB method contributes to the force applied by the object on the external fluid as well as the unsteady flow inside the virtual domain which is occupied by the object. These formulae are particularly important when the object in unsteady motion is solved in an inertial coordinate system. The formulae are adopted in the present two-dimensional (2D) numerical model, in which a SIMPLEC-type two-step computational scheme is introduced to solve the Navier-Stokes (N-S) equations. Several case studies, including the simulation of the vortex-induced vibration (VIV) of a circular cylinder, are carried out in this work. The agreement of the predicted results with the experimental and numerical data reported by other researchers proves the significance of these formulae.     

Linear stability analysis in fluid-structure interaction with transpiration. Part II: Numerical analysis and applications

This paper constitutes the numerical counterpart of the mathematical framework introduced in Part I. We address the problem of flutter analysis of a coupled fluid-structure system involving an incompressible Newtonian fluid and a reduced structure. We use the Linearization Principle approach developed in Part I, particularly suited for fluid-structure problems involving moving boundaries. Thus, the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity. This eigenproblem involves the linearized incompressible Navier-Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration interface conditions. The eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized Cayley transform and an implicit restarted Arnoldi method. Finally, we report three numerical experiments: a structure immersed in a fluid at rest, a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects. The numerical results are compared to former approaches and experimental data. The quality of these numerical results is very satisfactory and promising.