Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number (Re) flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50,000 in the literature; however, this paper can readily extend the maximum to 1000,000 with the above combination.     

A traffic flow lattice model considering relative current influence and its numerical simulation

<正>Based on Xue's lattice model,an extended lattice model is proposed by considering the relative current information about next-nearest-neighbour sites ahead.The linear stability condition of the presented model is obtained by employing the linear stability theory.The density wave is investigated analytically with the perturbation method.The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries(mKdV) equation.The simulation results are in good agreement with the analytical results,showing that the stability of traffic flow can be enhanced when the relative current of next-nearest-neighbour sites ahead is considered.     

A lattice hydrodynamical model considering turning capability

A new two-dimensional lattice hydrodynamic model considering the turning capability of cars is proposed. Based on this model, the stability condition for this new model is obtained by using linear stability analysis. Near the critical point, the modified KdV equation is deduced by using the nonlinear theory. The results of numerical simulation indicate that the critical point a c increases with the increase of the fraction p of northbound cars which continue to move along the positive y direction for c = 0.3, but decreases with the increase of p for c = 0.7. The results also indicate that the cars moving along only one direction (eastbound or northbound) are most stable.     

A higher order lattice BGK model for simulating some nonlinear partial differential equations

In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.     

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau (TDGL) equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.     

A semi-implicit lattice method for simulating flow

We propose a new semi-implicit lattice numerical method for modeling fluid flow that depends only on local primitive variable information (density, pressure, velocity) and not on relaxed upstream distribution function values. This method has the potential for reducing parallel processor communication and permitting larger time steps than the lattice-Boltzmann method. Several benchmark problems are solved to demonstrate the accuracy of the method.     

考虑驾驶员预估效应的交通流格子模型与数值仿真

考虑驾驶员的预估效应对车流的影响,提出了一个改进的一维交通流格子模型.基于线性稳定性理论得到了该模型的线性稳定性判据;运用非线性分析方法导出了描述交通阻塞相变时的mKdV方程.应用数值仿真验证了mKdV方程的解,研究表明适当考虑车流中预估效应的作用能够增强交通流稳定性,从而能有效抑制交通阻塞的形成. 关键词： 预估效应 交通流 格子模型 数值仿真     

A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect

We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world.Applying the linear stability theory,we obtain the linear stability condition of the model.Through nonlinear analysis,we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point.The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi-anticipation effect is considered.     

两车道交通流耦合格子模型与数值仿真

考虑两车道耦合效应的影响和换道效应,提出了改进的两车道交通流耦合格子模型.同时,改进了换道时的流量转移率,这样更符合实际交通情况.通过线性稳定性分析,得到了改进模型的稳定性条件.数值模拟结果也表明,模型通过考虑耦合作用信息,更好地再现了换道情况,同时也表明两车道间的耦合效应对两车道交通流存在不可忽视的影响.     

跨流域高超声速绕流环境Boltzmann模型方程统一算法研究

如何准确可靠地模拟从外层空间高稀薄流到近地面连续流的航天器高超声速绕流环境与复杂流动变化机理是流体物理的前沿基础科学问题. 基于对Boltzmann方程碰撞积分的物理分析与可计算建模, 确立了可描述自由分子流到连续流区各流域不同马赫数复杂流动输运现象统一的Boltzmann模型速度分布函数方程, 发展了适于高、低不同马赫数绕流问题的离散速度坐标法和直接求解分子速度分布函数演化更新的气体动理论数值格式, 建立了模拟复杂飞行器跨流域高超声速飞行热环境绕流问题的气体动理论统一算法. 对稀薄流到连续流不同Knudsen数0.002 ≤Kn_∞ ≤1.618、不同马赫数下可重复使用卫星体再入过程(110–70 km)中高超声速绕流问题进行算法验证分析, 计算结果与典型文献的Monte Carlo直接模拟值及相关理论分析符合得较好. 研究揭示了飞行器跨流域不同高度高超声速复杂流动机理、绕流现象与气动力/热变化规律, 提出了一个通过数值求解介观Boltzmann模型方程, 可靠模拟高稀薄自由分子流到连续流跨流域高超声速气动力/热绕流特性统一算法.     

The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms

Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two- and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied. Supported by the National Natural Foundation of China (Grant Nos. 40874077, 40504020, and 40536029) and the National Basic Research Program of China (Grant No. 2006CB806304)     

A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids

A new differential lattice Boltzmann equation (LBE) is presented in this work, which is derived from the standard LBE by using Taylor series expansion only in spatial direction with truncation to the second-order derivatives. The obtained differential equation is not a wave-like equation. When a uniform grid is used, the new differential LBE can be exactly reduced to the standard LBE. The new differential LBE can be applied to solve irregular problems with the help of coordinate transformation. The present scheme inherits the merits of the standard LBE. The 2-D driven cavity flow is chosen as a test case to validate the present method. Favorable results are obtained and indicate that the present scheme has good prospects in practical applications.     

Study on the unified algorithm for three-dimensional complex problems covering various flow regimes using Boltzmann model equation

The Boltzmann simplified velocity distribution function equation describing the gas transfer phenomena from various flow regimes will be explored and solved numerically in this study. The discrete velocity ordinate method of the gas kinetic theory is studied and applied to simulate the complex multi-scale flows. Based on the uncoupling technique on molecular movement and colliding in the DSMC method, the gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by extending and applying the unsteady time-splitting method from computational fluid dynamics. The Gauss-type discrete velocity numerical quadrature technique for different Mach number flows is developed to evaluate the macroscopic flow parameters in the physical space. As a result, the gas-kinetic numerical algorithm is established to study the three-dimensional complex flows from rarefied transition to continuum regimes. The parallel strategy adapted to the gas-kinetic numerical algorithm is investigated by analyzing the inner parallel degree of the algorithm, and then the HPF parallel processing program is developed. To test the reliability of the present gas-kinetic numerical method, the three-dimensional complex flows around sphere and spacecraft shape with various Knudsen numbers are simulated by HPF parallel computing. The computational results are found in high resolution of the flow fields and good agreement with the theoretical and experimental data. The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach to resolve the hypersonic aerothermodynamic problems with the complete spectrum of flow regimes from the gas-kinetic point of view of solving the Boltzmann model equation. Supported by the National Natural Science Foundation of China (Grant Nos. 90205009 and 10321002) and the National Parallel Computing Center     

A novel lattice model integrating the cooperative deviation of density and optimal flux under V2X environment

A novel lattice hydrodynamic model is proposed by integrating the cooperative deviation of density and optimal flux under vehicle to X (V2X) environment. According to the theoretical analysis, the stability conditions and the mKdV equations affected by the cooperative deviation of traffic information are explored. And the density wave, hysteresis loop and energy consumption of the traffic flow have been investigated via numerical simulation. The results indicate that the cooperative deviation of density and optimal flux can effectively alleviate the traffic congestion. More importantly, our new consideration can reduce fuel consumption and exhaust emission under the V2X environment.     

A mean—field approximation scheme containing the spatial parameter and its application to a surface—reaction—like cellular automaton model

Using an AB2 Surface-reaction-like cellular automaton model,we present a modified mean-field approximation scheme for describing some dynamic lattice models,in which a lattice freedom parameter N is introduced as a variable,We obtain the phase diagrams of the example model for linear,hexagonal,square and triangular lattices,and we reveal a second-order phase transiton which has not been found using using traditional approaches.     

纤维悬浮湍流的方程和解及其在管流中的应用

推导了纤维悬浮流的平均运动方程和纤维平均取向角的概率密度函数方程，提出了计算纤维平均取向角分布和悬浮流平均量与脉动量关联函数的逐级迭代方法。将推导的方程和提出的方法用于纤维悬浮管流场的计算并进行了相应的实验，计算和实验结果吻合很好。研究结果表明，在相同的压力降下，与没有纤维的牛顿流相比，纤维悬浮流具有较大的流量，因而纤维在流场中起着减阻的作用，减阻的量随着纤维浓度的增加而增大。在相同情况下，纤维悬浮流的相对湍流强度和雷诺应力比牛顿流小，这说明纤维能够抑制湍流，抑制的量与纤维的质量浓度成正比。     

多孔介质中流体流动及扩散的耦合格子Boltzmann模型

多孔介质中高Péclet数和大黏性比下混溶流体的流动和扩散广泛存在于二氧化碳驱油、化工生产等工业过程中.用数值方法对该问题进行研究时,关键在于如何正确描述高Péclet数和大黏性比下多孔介质内流体的行为.为此,提出了一种基于多松弛模型和格子动理模型的耦合格子Boltzmann模型.通过Chapman-Enskog分析,证明该模型能有效求解不可压Navier-Stokes方程和对流扩散方程.数值结果表明,该模型不仅具有二阶精度和良好的稳健性,而且对于高Péclet数和大黏性比的问题具有良好的数值稳定性,为模拟此类问题提供了有效工具.     

A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.     

考虑信号灯影响的交通流模型与数值模拟

基于信号灯交通系统中跟车行为的特点,改进了现有跟车方程,提出一个考虑信号影响的交通流模型.数值计算结果表明,该模型可以很好地再现车流的聚集与消散、停车波和启动波的演化规律及传播特性,证明模型是合理有效的. 关键词： 交通流模型 信号灯 停车波 启动波     

Three-dimensional finite-difference lattice Boltzmann model and its application to inviscid compressible flows with shock waves

In this paper, a three-dimensional (3D) finite-difference lattice Boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double-distribution-function approach. In the model, a density distribution function is adopted to model the flow field, while a total energy distribution function is adopted to model the temperature field. The discrete equilibrium density and total energy distribution functions are derived from the Hermite expansions of the continuous equilibrium distribution functions. The discrete velocity set is obtained by choosing the abscissae of a suitable Gauss–Hermite quadrature with sufficient accuracy. In order to capture the shock waves in compressible flows and improve the numerical accuracy and stability, an implicit–explicit finite-difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations. The model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1D to 3D. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.