一种新型光滑粒子动力学固壁边界施加模型

由于Lagrange粒子法的本质, 固壁边界条件的施加一直是光滑粒子动力学方法的难点之一. 本文从固壁边界的物理原理出发, 应用多层虚粒子表征固壁边界, 提出了一种新型固壁边界施加模型. 将虚粒子看作流体的扩展, 计算中虚粒子密度保持不变, 压力、速度等参数通过对流体粒子的插值获得, 虚粒子有条件的参与控制方程的计算, 对流体的密度/压力产生影响, 通过压力梯度隐式地表征壁面与流体之间的作用强度并对流体粒子施加沿壁面法线方向的斥力作用, 防止流体粒子对壁面的穿透. 数值算例测试结果表明, 与现有固壁边界施加方法相比, 本文方法更加符合流体与固壁边界作用的物理原理, 可以简单、有效地施加固壁边界条件, 方便地应用于具有复杂几何边界的问题, 获得稳定的流场形态、规则的粒子秩序及良好的速度、压力等参量的分布.     

基于速度源修正的浸入边界-晶格玻尔兹曼法研究仿生微流体驱动模型

浸入边界—晶格波尔兹曼法在流固耦合等复杂的流体系统中得到广泛的应用.本文采用基于速度源修正的浸入边界—晶格玻尔兹曼法,建立了仿生微流体驱动模型,创新性地将波动弹性体的速度引入晶格玻尔兹曼方程,避免了传统浸入边界—晶格玻尔兹曼法中浸入边界速度-结构变形-力之间的转换,提高了计算效率和准确率.研究了行波波动细丝对流场内流动速度和压力的影响,重点分析了驱动模型各项参数对微流体的驱动效果.研究结果表明:细丝长度、频率、振幅的增加引起出口处流量的增加;波长、流体粘滞系数以及细丝位置与出口处流量呈复杂的非线性关系.     

Steady state convergence acceleration of the generalized lattice Boltzmann equation with forcing term through preconditioning

Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature, requires a long time to attain steady state convergence, particularly at low Mach numbers due to the disparity in characteristic speeds of propagation of different quantities. In this paper, we present a preconditioned generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate steady state convergence to flows driven by external forces. The use of multiple relaxation times in the GLBE allows enhancement of the numerical stability. Particular focus is given in preconditioning external forces, which can be spatially and temporally dependent. In particular, correct forms of moment projections of source/forcing terms are derived such that they recover preconditioned Navier–Stokes equations with non-uniform external forces. As an illustration, we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic Prandtl numbers, which imposes Lorentz forces on the flow of conducting fluids. Computational studies, particularly in three-dimensions, for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning. In addition, the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation.     

Lattice Boltzmann simulation of solid particles suspended in fluid

The lattice Boltzmann method, an alternative approach to solving a fluid flow system, is used to analyze the dynamics of particles suspended in fluid. The interaction rule between the fluid and the suspended particles is developed for real suspensions where the particle boundaries are treated as no-slip impermeable surfaces. This method correctly and accurately determines the dynamics of single particles and multi-particles suspended in the fluid. With this method, computational time scales linearly with the number of suspensions,N, a significant advantage over other computational techniques which solve the continuum mechanics equations, where the computational time scales asN ³. Also, this method solves the full momentum equations, including the inertia terms, and therefore is not limited to low particle Reynolds number.     

On the damping of unsteady flow by compliant boundaries

This paper concerns unsteady motion of an incompressible inviscid fluid near a flexible surface which, in responding to the surface pressure field, absorbs energy. The modification of the flow consequent on energy removal at the boundaries is examined. Energy absorption always occurs when the mechanical surface properties include an element of dissipation. But surface dissipation is not essential; surface waves have a similar property. Unsteady fluid induced forces excite surface waves which carry with them energy that must have originated in the flow. The question of how flow characteristics change as energy is gradually given up to the boundary is examined through a particular model problem from which it becomes evident that surface motion draws vorticity towards the surface. The model chosen is that of a rectilinear vortex adjacent to a weakly responding boundary. Surface motion induces a velocity perturbation which is shown to move the vortex towards the surface whenever the fluid gives energy to that surface.     

An improved immersed boundary-lattice Boltzmann method for simulating three-dimensional incompressible flows

The recently proposed boundary condition-enforced immersed boundary-lattice Boltzmann method (IB-LBM) [14] is improved in this work to simulate three-dimensional incompressible viscous flows. In the conventional IB-LBM, the restoring force is pre-calculated, and the non-slip boundary condition is not enforced as compared to body-fitted solvers. As a result, there is a flow penetration to the solid boundary. This drawback was removed by the new version of IB-LBM [14], in which the restoring force is considered as unknown and is determined in such a way that the non-slip boundary condition is enforced. Since Eulerian points are also defined inside the solid boundary, the computational domain is usually regular and the Cartesian mesh is used. On the other hand, to well capture the boundary layer and in the meantime, to save the computational effort, we often use non-uniform mesh in IB-LBM applications. In our previous two-dimensional simulations [14], the Taylor series expansion and least squares-based lattice Boltzmann method (TLLBM) was used on the non-uniform Cartesian mesh to get the flow field. The final expression of TLLBM is an algebraic formulation with some weighting coefficients. These coefficients could be computed in advance and stored for the following computations. However, this way may become impractical for 3D cases as the memory requirement often exceeds the machine capacity. The other way is to calculate the coefficients at every time step. As a result, extra time is consumed significantly. To overcome this drawback, in this study, we propose a more efficient approach to solve lattice Boltzmann equation on the non-uniform Cartesian mesh. As compared to TLLBM, the proposed approach needs much less computational time and virtual storage. Its good accuracy and efficiency are well demonstrated by its application to simulate the 3D lid-driven cubic cavity flow. To valid the combination of proposed approach with the new version of IBM [14] for 3D flows with curved boundaries, the flows over a sphere and torus are simulated. The obtained numerical results compare very well with available data in the literature.     

Accurate Solutions of the Navier-Stokes Equations Despite Unknown Outflow Boundary Data

A very common procedure when constructing boundary conditions for the time-dependent Navier-Stokes equations at artificial boundaries is to extrapolate the solution from grid points near the boundary to the boundary itself. For supersonic outflow, where all the characteristic variables leave the computational domain, this leads to accurate results. In the case of subsonic outflow, where one characteristic variable enters the computational domain, one cannot in general expect accurate solutions by this procedure. The problem with outflow boundary operators of extrapolation type at artificial boundaries with errors in the boundary data of order one will be investigated. Both the problem when the artificial outflow boundary is located in essentially uniform flow and the situation when the artificial outflow boundary is located in a flow field with large gradients are discussed. It will be shown, that in the special case when there are large gradients tangential to the boundary, extrapolation methods can be used even in the subsonic case.     

A multirate time integrator for regularized Stokeslets

The method of regularized Stokeslets is a numerical approach to approximating solutions of fluid–structure interaction problems in the Stokes regime. Regularized Stokeslets are fundamental solutions to the Stokes equations with a regularized point-force term that are used to represent forces generated by a rigid or elastic object interacting with the fluid. Due to the linearity of the Stokes equations, the velocity at any point in the fluid can be computed by summing the contributions of regularized Stokeslets, and the time evolution of positions can be computed using standard methods for ordinary differential equations. Rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized Stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid. For problems with boundaries modeled by springs with large spring constants, the resulting ordinary differential equations become stiff, and hence the time step for explicit time integration methods is severely constrained. Unfortunately, the use of standard implicit time integration methods for the method of regularized Stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems. Here, an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method. The multirate methods are higher-order methods that treat different portions of the ODE explicitly with different time steps depending on the stiffness of each component. Numerical examples on two nontrivial three-dimensional problems demonstrate the increased efficiency of the multi-explicit approach with no significant increase in numerical error.     

A differentially interpolated direct forcing immersed boundary method for predicting incompressible Navier–Stokes equations in time-varying complex geometries

A dispersion-relation-preserving dual-compact scheme developed in Cartesian grids is applied together with the immersed boundary method to solve the flow equations in irregular and time-varying domains. The artificial momentum forcing term applied at certain points in cells containing fluid and solid allows an imposition of velocity condition to account for the motion of solid body. We develop in this study a differential-based interpolation scheme which can be easily extended to three-dimensional simulation. The results simulated from the proposed immersed boundary method agree well with other numerical and experimental results for the chosen benchmark problems. The accuracy and fidelity of the IB flow solver developed to predict flows with irregular boundaries are therefore demonstrated.     

Implementation of nonreflecting boundary conditions for the nonlinear Euler equations

Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier–Bessel modes. This leads to an ‘exact’ nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier–Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.     

Accounting for convective effects in zero-Mach-number thermoacoustic models

This paper presents a methodology to account for some mean-flow effects on thermoacoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M=0 assumption, a nonzero-Mach-number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a “delayed entropy coupled boundary condition” (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating-pressure equation.     

三角形网格上多介质流动问题界面处理方法

多介质流动问题的求解一般是在结构网格上实现,而三角形网格对于复杂计算区域具有更好的适应性,本文结合rGFM方法,给出三角形网格上多介质流动问题界面处理方法.利用level-set方法跟踪界面,在界面处构造Riemann问题,得到界面处流体准确的流动状态.通过定义界面边界条件,将多介质流动问题转化为单介质流动问题,利用高精度RKDG方法求解.采用多个算例验证该方法的稳健性和有效性,结果表明该方法能准确捕捉界面和激波的位置,保持界面清晰.     

Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation

This article presents numerical analysis and practical considerations for three-dimensional flow computation using an implicit immersed boundary method. The Euler equations, or half a step of the Navier–Stokes equations when using fractional step algorithms, are investigated in their vorticity formulation. The context of flow computation around an arbitrarily shaped body is especially investigated.In conventional immersed boundary methods using vorticity, singular vortex are dispatched over the body surface. In the present study, one prefers using sources of potential velocity field, dispatched on the body, whose nature is not vorticity. Such a formulation is compatible to the Euler equations. In practice, these sources of potential flow produce a velocity through this surface, aiming in practice at cancelling a flow-through velocity.This article focuses on the use of the source-to-flow-through linear application, its properties being the key points for fast convergence. Its self-adjointness, or lack thereof, conditioning and preconditioning aspects are investigated. It follows that computing a velocity field with no-flow-through conditions in complex geometry, when using the source-to-flow-through linear application, can be achieved for 4/3 of the computational cost of standard Poisson equation in a Cartesian box.The robustness of immersed boundaries is especially interesting when used together with vortex-in-cell methods, well known for their robustness in time and their ability to compute accurately convective effects. A few examples, based on real-world geometries, illustrate the method capabilities.     

层状介质时域有限差分方法斜入射平面波引入新方式

应用二维时域有限差分方法分析层状介质中的目标散射时,在总场-散射场边界斜入射平面波源用常规方法难以引入,因为在总场-散射场边界处设置的入射波实际上包含了入射脉冲以及各分层界面的反射和多次反射.为解决这个问题,提出了斜入射平面波的混合引入方式,即对总场-散射场的四个边界面采取不同的处理方式.对于总场-散射场的纵向侧边界,用含有斜入射角度的修正一维时域有限差分方法,只要在自由空间位置加入入射脉冲就会自行产生由各分层界面形成的反射波,包括多次反射.同时,把纵向总场-散射场侧边界向下延伸,使得总场-散射场下边界位于完全匹配层内,这样透射波和散射波均为外向行波而被吸收.对于总场-散射场的上边界,由于完全位于自由空间中,边界上各点的入射波将是总场-散射场纵向边界角点处入射波的带有时间延迟的复制.数值模拟结果表明了本文所提出方法的正确性和有效性. 关键词： 时域有限差分 层状介质 斜入射平面波 修正一维麦克斯韦方程     

Acoustic-gravity waves in atmospheric and oceanic waveguides

A theory of guided propagation of sound in layered, moving fluids is extended to include acoustic-gravity waves (AGWs) in waveguides with piecewise continuous parameters. The orthogonality of AGW normal modes is established in moving and motionless media. A perturbation theory is developed to quantify the relative significance of the gravity and fluid compressibility as well as sensitivity of the normal modes to variations in sound speed, flow velocity, and density profiles and in boundary conditions. Phase and group speeds of the normal modes are found to have certain universal properties which are valid for waveguides with arbitrary stratification. The Lamb wave is shown to be the only AGW normal mode that can propagate without dispersion in a layered medium.     

FVM-MD耦合算法在碳纳米管绕流中的应用

本文采用有限容积法(FVM)-分子动力学(MD)耦合算法,模拟研究了碳纳米管绕流现象.在液体流动方向和垂直于流动的方向同时用非周期性边界条件处理,相比于传统的周期性边界条件,更准确地描述了液体流动.耦合方法与纯MD方法进行比较的结果显示耦合方法不但可以节省计算时间,而且在保证精确刻画局部微观细节的前提下,能更加准确地描...     

Using streamlines to visualize acoustic energy flow across boundaries

For spherical waves that radiate from a point source in a homogeneous fluid and propagate across a plane boundary into a dissimilar homogeneous fluid, the acoustic field may differ significantly from the geometric acoustic approximation if either the source or receiver is near the interface (in acoustic wavelengths) or if the stationary phase path is near the critical angle. In such cases, the entire acoustic field must be considered, including inhomogeneous waves associated with diffraction (i.e., those components that vanish with increasing frequency). The energy flow from a continuous-wave monopole point source across the boundary is visualized by tracing acoustic streamlines: those curves whose tangent at every point is parallel to the local acoustic intensity vector, averaged over a wave cycle. It is seen that the acoustic energy flow is not always in line with the "Snell's law" or stationary phase path. Also, plots of acoustic energy streamlines do not display unusual behavior in the vicinity of the critical angle. Finally, it is shown that there exists a law of refraction of acoustic energy streamlines at boundaries with density discontinuities analogous to Snell's law of refraction of ray paths across sound speed discontinuities. Examples include water-to-seabed transmission and water-to-air transmission.     

The selection of layer thicknesses to control acoustic radiation force profiles in layered resonators

Ultrasonic standing waves can be used to generate radiation forces on particles within a fluid. A number of authors have derived detailed representations of these forces but these are most commonly applied using an approximation to the energy distribution based upon an idealized standing wave within a mode based upon rigid boundaries. An electro-acoustic model of the acoustic energy distribution within a standing wave with arbitrary thickness boundaries has been expanded to model the radiation force on an example particle within the acoustic field. This is used to examine the force profile on a particle at resonances other than those predicted with rigid boundaries, and with pressure nodes at different positions. A simple analytical method for predicting modal conditions for combinations of frequencies and layer thickness characteristics is presented, which predicts that resonances can exist that will produce a pressure node at arbitrary positions in the fluid layer of such a system. This can be used to design resonators that will drive particles to positions other than the center of the fluid layer, including the fluid/solid boundary of the layer, with significant potential applications in sensing systems. Further, the model also predicts conditions for multiple subwavelength resonances within the fluid layer of a single resonator, each resonance having different nodal planes for particle concentration.     

Free surface waves in wall-bounded granular flows

We report free-surface waves in granular flows near boundaries in an inclined chute. The chevron-shaped traveling waves spontaneously develop at inclinations close to the angle of repose for both steady and accelerating flows. Two distinct regimes are characterized by internal angle and frequency variations. Experimental measurements indicate that subsurface circulation driven by velocity gradients near frictional walls plays a central role in the pattern formation mechanism, suggesting that wave generation is controlled by the granular analog of a fluid boundary layer.