Lattice Boltzmann simulations of flow past a cylindrical obstacle

We present lattice Boltzmann simulations of flow past a cylindrical obstacle. Our study is based on the Lévy walk model of turbulence in a lattice Boltzmann model. We discuss pressure around the cylinder with laminar and turbulent incident flows, as well as the dependence of the von Karman street on the analog of integral scale in our model.     

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.     

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.     

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.     

Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid

A lattice Boltzmann method is developed to simulate three-dimensional solid particle motions in fluids. In the present model, a uniform grid is used and the exact spatial location of the physical boundary of the suspended particles is determined using an interpolation scheme. The numerical accuracy and efficiency of the proposed lattice Boltzmann method is demonstrated by simulating the sedimentation of a single sphere in a square cylinder. Highly accurate simulation results can be achieved with few meshes, compared with the previous lattice Boltzmann methods. The present method is expected to find applications on the flow systems with moving boundaries, such as the blood flow in distensible vessels, the particle－flow interaction and the solidification of alloys.     

Lattice Boltzmann方法模拟多孔介质Klinkenberg效应

格子Boltzmann数值模拟方法是研究复杂的多孔介质结构特别是Klinkenberg效应的有效方法之一，对处理复杂边值问题尤其有效，用格子Boltzmann方法研究了气流穿越多孔介质问题，并将数值计算结果与实验结果进行了比较，结果表明格子Boltzmann方法是数值模拟气流穿越多孔介质问题的有效方法之一。     

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann (LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time (SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time (MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.     

Boundary conditions for lattice Boltzmann simulations

A heuristic interpretation of no-slip boundary conditions for lattice Boltzmann and lattice gas simulations is developed. An improvement is suggested which consists of including the wall nodes in the collision operation.     

椭圆柱体在牛顿流体中运动的格子Boltzmann方法模拟

用格子Boltzmann方法建立了椭圆柱体的二维动力学模型，利用所建立的模型，数值模拟了 牛顿流体中不同形状的椭圆柱体在相同初始条件下的运动和同一椭圆柱体在不同初始条件下 的运动，并通过比较相同条件下圆柱体的运动，讨论了椭圆柱体二维运动的特征，得到了一 些有意义的结果. 关键词： 格子Boltzmann方法 椭圆柱体 牛顿流体     

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.     

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.     

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.     

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.     

格子Boltzmann方法中三维运动边界的统一模型

格子Boltzmann方法(LBM)中边界条件的处理很复杂,在现有的边界条件处理方法中,动力学格式能够精确满足宏观边界条件,但由于要解一个不定方程,必须引入附加假设确保方程非奇异.作为动力学格式和反弹格式的一种扩展,提出一种处理三维任意速度运动边界的统一模型,其中人口速度和固体壁面速度是该模型的特殊情形.给出用于三维15速度的表达式.为了检验该模型,模拟对角顶盖驱动三维空腔流,并将结果与有限差分法计算的结果进行比较,说明所提出的统一模型是合理可行的.     

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.     

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. 90 (2010) 54003]. We discuss the reason why the Gram-Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 (2004) 035701(R)] is only valid in subsonic flows.The von Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer-Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.     

Extended Lattice Boltzmann Model

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.     

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.     

格子Boltzmann方法模拟双液滴撞击液膜的流动过程

采用单相自由面格子Boltzmann方法中流场计算,自由面条件和表面张力处理方法,研究双液滴撞击液膜的流动过程,实现对垂直间隔的两液滴相继撞击液膜流动过程的模拟.数值结果表明,液滴相继冲击液膜时,液滴间上下距离对液膜状态有很大的影响,液滴间距不同,液膜形状会出现很大差异.数值结果与实验结论定性一致.     

A improved incompressible lattice Boltzmann model for time-independent flows

It is well known that the lattice Boltzmann equation method (LBE) can model the incompressible Navier-Stokes (NS) equations in the limit where density goes to a constant. In a LBE simulation, however, the density cannot be constant because pressure is equal to density times the square of sound speed, hence a compressibility error seems inevitable for the LBE to model incompressible flows. This work uses a modified equilibrium distribution and a modified velocity to construct an LBE which models time-independent (steady) incompressible flows with significantly reduced compressibility error. Computational results in 2D cavity flow and in a 2D flow with an exact solution are reported.