Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

We discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice Boltzmann model. Their accuracy is investigated in the case of Couette flow by considering the slip regime. The best results are recovered with versions 2 and 3, which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain. Version 2 is found to be more economical since it involves no interpolation procedure. This version was thereafter used to investigate the temperature profile in Couette flow for various values of Prandtl number, as well as the capability of the thermal LB model to capture the Knudsen minimum in Poiseuille flow.     

An Effective Method on Two-Dimensional Lattice Boltzmann Simulations with Moving Boundaries

We propose a lattice Boltzmann scheme for two-dimensional complex boundaries moving in fluid flow. The hydrodynamic forces exerting on the moving boundaries are calculated based on a stress-integration method proposed before, but the extrapolation procedure is avoided, and the stability of this model is improved. The accuracy and robustness are demonstrated by numerical simulations of a circular particle settling in a twodimensional vertical channel. The numerical convergence is studied by varying the time-step and the dimensionless particle sizes.     

An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective.     

Lattice Boltzmann Simulations of Particle-Particle Interaction in Steady Poiseuille Flow

The moving behaviour of two- and three-particles in a pressure-driven flow is studied by the lattice Boltzmann simulation in two dimensions. The time-dependent values, including particles＇ radial positions, translational velocities, angular velocities, and the x-directional distance between the particles are analysed extensively. The effect of flow Reynolds number on particle motion is also investigated numerically. The simulation results show that the leading particle equilibrium position is closer to the channel centre while the trailing particle equilibrium position is closer to the channel wall. If Reynolds number Re is less than 85.30, the larger flow Reynolds number results in the smaller x-directional equilibrium distance, otherwise the x-directional distance increases almost linearly with the increase of time and the particles separate finally. The simulation results are helpful to understand the particle-particle interaction in suspensions with swarms of particles.     

General relativistic Boltzmann equation, I: Covariant treatment

This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions. Thereupon, the general relativistic Boltzmann equation, to be obeyed by this function, is derived. The use of either contravariant or covariant momenta leads to different, but equivalent, forms of the equation.The results of the present article are covariant, but not manifestly covariant. The transition to a manifestly covariant treatment, on the basis of off-shell momenta, is given in the second article.     

General relativistic Boltzmann equation, II: Manifestly covariant treatment

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p²=m²c². Due to this restriction, the resulting Boltzmann equation, although covariant, turned out to be not manifestly covariant. In the present article we switch from mass-shell momenta to off-shell momenta, and thereby arrive at a Boltzmann equation that is manifestly covariant.     

Effect of Temperature on the Void Growth in Pure Aluminium at High Strain-Rate Loading

With the environment temperature varying from 273 K to 773 K, the dynamic process of void growth in pure aluminium at high strain-rate loading is calculated based on the dynamic growth equation of a void with internal pressure. The result shows that the effect of temperature on the growth of void should be emphasized. Because the initial pressure of void with gas will increase and the viscosity of materials will decrease with the rising of temperature, the growth of void is accelerated. Furthermore, material inertia restrains the growth of void evidently when the diameter exceeds 10 μm. The effect of surface tension is very weak in the whole process of void growth.     

Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation

Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local “fixes” for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolved rather that reconstructed at every timestep, resulting in a compact stencil. Interface states are evolved using Riemann invariants containing all transverse derivative information. The conservation laws are updated in an unsplit fashion, making the scheme fully multidimensional. Divergence-free evolution of the magnetic field is maintained using the higher order-accurate constrained transport technique of Gardiner and Stone. The accuracy and stability of the scheme is documented against a bank of standard test problems drawn from the literature. The method is applied to numerical simulation of supersonic MHD turbulence, which is important for many problems in astrophysics, including star formation in dark molecular clouds. PPML accurately reproduces in three-dimensions a transition to turbulence in highly compressible isothermal gas in a molecular cloud model. The low dissipation and wide spectral bandwidth of this method make it an ideal candidate for direct turbulence simulations.     

Using Digital Imaging to Characterize Threshold Dynamic Parameters in Porous Media Based on Lattice Boltzmann Method

Digital images (DI) and lattice Boltzmann method (LBM) are used to characterize the threshold dynamic parameters of porous media. Two-dimensional representations of the porous structure are reconstructed from segmentation of digital images obtained from a series of tiny samples. The threshold pressure gradients and threshold Péclet numbers are researched on seven test samples by using LBM. Numerical results are in agreement with that obtained by integrating Darcy’s law. The results also indicate that fluids can flow through porous media only if the fluid force is large enough to overcome threshold pressure gradient in porous media. One synthetic case is used to further illustrate the applicability of the proposed technique. In addition, the dynamical rules in our model are local, therefore it can be run on parallel computers with well computational efficiency.     

Two generalizations of the Boltzmann equation

We connect two different extensions of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities or equivalently by using nontrivial energy composition rules in the energy conservation constraint part. Direct transformation formulas between key functions of the two approaches are given.     

Molecular dynamics simulation of AFM studies of a single polymer chain

Single polymer chain force-extension behavior measured by Atomic Force Microscopy (AFM) was interpreted by molecular dynamics (MD) simulation performed by applying a bead-spring (coarse-graining) model in which the bond potential function between adjacent beads is described by a worm-like chain (WLC) model. Simulation results indicate that caution should be applied when interpreting experimental AFM data, because the data vary depending on the point of AFM tip-polymer chain attachment. This approach offers an effective way for eventual analysis of the mechanical behavior of complex polymer networks.     

Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 1999     

Simulation of microchannel flow using the lattice Boltzmann method

For microchannel flow simulation, the slip boundary model is very important to guarantee the accuracy of the solution. In this paper, a new slip model, the Langmuir slip model, instead of the popularly used Maxwell slip model, is incorporated into the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the rarefied gas flow. Its feasibility and accuracy are examined by simulations of microchannel flow. Although, for simplicity, in this paper our recently developed LB model is used to solve the flow field, this does not prevent the present boundary scheme from easily incorporating other LB models, for example the more advanced collision model with multiple relaxation times. In addition, the existing non-equilibrium extrapolation LB boundary scheme for macroscopic flows can be recovered naturally from the present scheme when the Knudsen number .     

Empirical evidences of a common multifractal signature in economic, biological and physical systems

Recent developments in microcanonical multifractal formalism have lead to a sensible improvement in the numerical techniques for the determination of the multifractal characteristics of real signals. With the aid of these techniques, we have found empirical evidence of a common multifractal signature in six very different systems, ranging from stock market time series to sea surface temperature records. These systems are not only found to be multifractal, but their singularity spectra are coincident. We propose an explanation of this striking coincidence in terms of a cascade process and analyze its consequences.     

Boltzmann simulation of a storage ring laser

A numerical technique is described, which follows the motion of the entire electron distribution in a storage ring laser. The laser gain and electron distribution parameters such as energy spread, bunch length, damping rates, and containment time are discussed, both with and without the use of the gain expansion technique. The limits of validity of the onedimensional approximation are defined.     

Molecular dynamics simulation of femtosecond ablation and spallation with different interatomic potentials

Fast heating of target material by femtosecond laser pulse (fsLP) with duration τ_L∼40-100 fs results in the formation of thermomechanically stressed state. Its unloading may cause frontal cavitation of subsurface layer at a depth of 50 nm for Al and 100 nm for Au. The compression wave propagating deep into material hits the rear-side of the target with the formation of rarefaction wave. The last may produce cracks and rear-side spallation. Results of MD simulations of ablation and spallation of Al and Au metals under action fsLP are presented. It is shown that the used EAM potentials (Mishin et al. and our new one) predict the different ablation and spallation thresholds on absorbed fluence in Al: ablation F_a=60{65} mJ/cm²and spallation F_s=120{190} mJ/cm², where numbers in brackets { } show the corresponding values for Mishin potential. The strain rate in spallation zone was 4.3×10⁹ 1/s at spallation threshold. Simulated spall strength of Al is 7.4{8.7} GPa, that is noticeably less than 10.3{14} GPa obtained from acoustic approximation with the use of velocity pullback on velocity profile of free rear surface. The ablation threshold F_a≈120 mJ/cm² and crater depth of 110 nm are obtained in MD simulations of gold with the new EAM potential. They agree well with experiment.     

Periodic Homoclinic Wave of （1＋1）-Dimensional Long-Short Wave Equation

The exact periodic homoclinic wave of （1＋1）D long-short wave equation is obtained using an extended homoclinic test technique. This result shows complexity and variety of dynamical behaviour for a （1＋1）-dimensional long-short wave equation.