Thermal equation of state for lattice Boltzmann gases

The Galilean invariance and the induced thermo-hydrodynamics of the lattice Boltzmann Bhatnagar--Gross--Krook model are proposed together with their rigorous theoretical background. From the viewpoint of group invariance, recovering the Galilean invariance for the isothermal lattice Boltzmann Bhatnagar--Gross--Krook equation (LBGKE) induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman--Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method （LBM） is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non- negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman-Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

多孔介质内混溶流体间粘性指进现象的格子Boltzmann模型

提出一个模拟多孔介质内混溶流体间粘性指进现象的格子Boltzmann模型.采用双分布函数分别求解压力场和浓度场.在浓度场平衡态分布函数中引入与浓度扩散相关的参数.通过调节参数,使粒子碰撞过程中的松弛时间保持恒定.模拟了粘度相同的流体间的混相驱替问题.不同网格下的模拟结果均与解析解吻合良好,验证了模型的可行性.进一步研究粘度比和贝克莱数(Pe)对粘性指进现象的影响.结果显示,增大粘度比会促进"手指"的增长.当粘度比不变时,存在Pe的临界值.当Pe超过临界值时,"手指"前缘会出现分裂现象.对横向平均浓度场的研究显示,混合区域的长度随时间的变化分为两个阶段,它首先随着t^1/2成线性增长,然后随着t成线性增长.     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional （31）） Lattice Boltzmann （LB） model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 （2004） 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative （NND） scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, （i） Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; （ii） reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high-speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara [Phys. Rev. E 69 (2004) 056702]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model isvalidated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

激励介质中非线性化学波的格子Boltzmann模型

构造了用于非线性化学波的格子Boltzmann模型.通过设置无对流速度场,使用多重尺度和Chapman Enskog展开,得到了平衡态分布函数的各向同性解.算例考虑了用划痕起搏,在ε²尺度上给出了Selkov系统的模拟结果,再现了远离热力学平衡态的螺旋波结构的经典结果,并与传统数值方法及实验结果进行了比较.     

Lattice Boltzmann simulation of transverse wave travelling in Maxwell viscoelastic fluid

A nine-velocity lattice Boltzmann method for Maxwell viscoelastic fluid is proposed. Travelling of transverse wavein Maxwell viscoelastic fluid is simulated. The instantaneous oscillating velocity, transverse shear speed and decay rateagree with theoretical results very well.     

辐射传输的格子Boltzmann模拟

辐射动力学理论是描述辐射传输是重要手段,基于此,本文建立了辐射能和辐射动量守恒方程,并基于Chapman-Enskog多尺度展开方法实现了从辐射传输Boltzmann方程到宏观方程的推导,进而建立了适于一维辐射传输的2分量格子Boltzmann模型。数值结果与精确解吻合较好,表明本文提出的LBM方法具有很好的准确性和稳...     

微通道内气体流动的格子Boltzmann方法研究

采用格子Boltzmann方法模拟了微通道在滑移区内不同Knudsen数下的微气体Poiseuille流,分析了微气体流动的速度分布以及流量与压降的关系,并给出了相对滑移长度和Poiseuille数随Knudsen数的变化特性。研究结果表明,微气体Poiseuille流的速度轮廓呈抛物线分布,但是边界速度大于0,出现速...     

一个三维多松弛时间全速域格子Boltzmann模型

构建一个既适用于低速不可压流体又适用于高速可压缩流体的三维自由参数多松弛时间格子Boltzmann模型.模型中,根据SO（3）群的不可约表述基函数构造转化矩阵,根据恢复可压Navier-Stokes方程的需要选取非守恒矩平衡值.通过von Neumann稳定性分析模型参数对数值稳定性的影响,并给出建议选择范围.模型经过基准问题的验证,模拟结果与解析解及其它数值结果符合较好.     

Diffusion Lattice Boltzmann Scheme on a Orthorhombic Lattice

We present a diffusion lattice Boltzmann (DLB) scheme which is derived from first principles. As opposed to the traditional lattice BGK schemes the DLB is valid for orthorhombic lattices and it has two eigenvalues of the collision operator. It is shown that the diffusion coefficient depends only on one eigenvalue of the collision operator. Hence, the DLB scheme can be optimized with means of the additional eigenvalue of the collision operator and with different lattice spacing along the principal axes. The properties of the DLB scheme concerning consistency, stability, and accuracy are studied with eigenmode analysis. This analysis shows that the DLB scheme is consistent with diffusion for a wide range of diffusion coefficients, it has unconditional stability, and that it has third-order accuracy. Furthermore, it is shown that accuracy is improved by setting the additional eigenvalue to zero and by densifying the lattice spacing along the direction of the density gradient.     

A Lattice Boltzmann Model for Anisotropic Crystal Growth from Melt

We coupled the lattice Boltzmann method with enhanced collisions for hydrodynamics with a model for the anisotropic liquid/solid phase transition. The model is based on a simple reaction model. As a test we have performed calculations for dendritic growth of a crystal into an undercooled melt.     

Highly Efficient Lattice Boltzmann Model for Compressible Fluids:Two-Dimensional Case

We present a highly efficient lattice Boltzmann model for simulatingcompressible flows. This model is based on the combination of an appropriatefinite difference scheme, a 16-discrete-velocity model [Kataoka andTsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion anddissipation terms. The dispersion term effectively reduces the oscillationat the discontinuity and enhances numerical precision. The dissipation termmakes the new model more easily meet with the von Neumann stabilitycondition. This model works for both high-speed and low-speed flows witharbitrary specific-heat-ratio. With the new model simulation results for thewell-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation ofstate or free-energy functional, the new model has the potential tostudythe complex procedure of shock wave reaction on porous materials.     

用晶格玻尔兹曼方法研究颗粒在涡流中的运动

用晶格玻尔兹曼方法研究小颗粒在涡流中的运动.涡流由流经空腔的流体产生.用动量交换法和压力张量积分法计算颗粒在涡流中的运动轨迹、速度和角速度.最后用张量积分法计算两个不同半径的颗粒在涡流中的运动. 关键词： 晶格玻尔兹曼方法 涡流 颗粒     

Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid

We define a lattice Boltzmann model of solid, deformable suspensions immersed in a fluid itself described in terms of the lattice Boltzmann method. We discuss the rules governing the internal dynamics of the solid object as well as the rules specifying the interaction between solid and fluid particle. We perform a numerical drag experiment to validate the model. Finally we consider the case of a population of flexible chains in suspension in a shear stress flow and study the influence on the velocity profile.     

格子Boltzmann守恒型非平衡态的外推边界

针对非平衡态外推边界处理方法在某些条件下发生质量泄漏的问题,结合质量守恒定律对其进行修正,建立一种新的质量守恒型的边界处理格式.其基本思想是在边界处定义一个虚拟密度来修正平衡态分布函数,使得系统质量守恒.以重力作用下的密度场及磁流体模拟问题为例,利用该格式进行分析,讨论质量泄露问题的本质及各种因素的影响.通过对三种典型的流动:二维Poiseuille流、Couette流、Womersley流的模拟,验证该边界格式的计算精度和稳定性.     

液滴撞击液膜过程的格子Boltzmann方法模拟

本文采用格子Boltzmann方法对液滴撞击液膜过程进行了研究, 主要考察了雷诺数(Re)、韦伯数(We)、相对液膜厚度 (h) 以及表面张力 (σ) 等物理参数对界面运动过程的影响. 首先, 随着Re数和We数的增加, 可以明显观察到液滴撞击液膜过程中形成的皇冠状水花以及卷吸现象; 当Re数较大时, 液体会发生飞溅, 由液体飞溅形成的小液滴则会继续下落, 并与液膜再次发生碰撞. 其次, 当相对液膜厚度较小时, 液滴撞击液膜并最终导致液膜断裂; 然而随着相对液膜厚度的增大, 尽管撞击过程溅起的液体会越来越多, 但是液膜并不会发生断裂. 再次, 随着表面张力的增大, 界面变形阻力增大, 撞击过程中产生的界面形变也逐渐减弱. 最后还发现皇冠(由液滴溅起形成)半径r 随时间满足r/(2R) ≈ α√Ut/(2R), 这一结果与已有结论是一致的.