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Multiscale Lattice Boltzmann schemes for fluid dynamic applications are described and their efficiency is discussed in terms of accuracy and computational cost. A novel application to axial compressor flows is proposed. Conditions on periodic boundaries have been appropriately developed. Our preliminary results indicate that these schemes hold good potential for the simulation of fluid flows in turbomachines.

An approach to lattice Boltzmann simulation is described, which makes a direct connection between classical kinetic theory and contemporary lattice Boltzmann modeling methods. This approach can lead to greater accuracy, improved numerical stability and significant reductions in computational needs, while giving a new philosophical point of view to lattice Boltzmann calculations for a large range of applications.

This paper investigates the possibility to reduce the compressibility of lattice Boltzmann fluid models by introducing a repulsive force between nearest neighbor lattice Boltzmann particles. This new interaction is based on the Shan–Chen model. The interest of this approach is that it implements the physical mechanism responsible for the incompressibility of real fluids and retains the natural interpretation of the fluid density and fluid momentum. The new state equation shows that the compressibility factor decreases as the repulsive interaction increases. However, numerical instabilities limit the value of the acceptable repulsion. We investigate several situations, such as the Poiseuille flow with pressure gradient, a static fluid subject to gravity and the Womersley flow to evaluate the benefits of our approach. Globally, the compressibility of lattice Boltzmann fluids can be reduced by a factor of 4.

In the diffusion-limited aggregation (DLA) model, pioneered by Witten and Sander (Phys. Rev. Lett.47, 1400 (1981)), diffusing particles irreversibly attach to a growing cluster which is initiated with a single solid seed. This process generates clusters with a branched morphology. Advection–diffusion-limited aggregation (ADLA) is a straightforward extension to this model, where the transport of the aggregating particles not only depends on diffusion, but also on a fluid flow. The authors studying two-dimensional and three-dimensional ADLA in laminar flows reported that clusters grow preferentially against the flow direction. The internal structure of the clusters was mostly reported to remain unaffected, except by Kaandorp et al. (Phys. Rev. Lett.77, 2328 (1996)) who found compact clusters "as the flow becomes more important". In the present paper we present three-dimensional simulations of ADLA. We did not find significant effects of low Reynolds-number advection on the cluster structure. The contradicting results by Kaandorp et al. (1996) were recovered only when the relaxation into equilibrium of the advection–diffusion field was too slow, in combination with the synchronous addition of multiple particles.

The origin of the spurious interface velocity in finite difference lattice Boltzmann models for liquid–vapor systems is related to the first order upwind scheme used to compute the space derivatives in the evolution equations. A correction force term is introduced to eliminate the spurious velocity. The correction term helps to recover sharp interfaces and sets the phase diagram close to the one derived using the Maxwell construction.

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re~O(10) to Re≤1000 was predicted by a single simulation algorithm.^1–5

Gas–gas mixing layers are important in many practical applications including transport of pollutants in smoke plumes and air–fuel mixing in combustion. In this paper, mixing layers are studied by conducting direct numerical simulations using a lattice Boltzmann model for binary fluids. The binary fluid model can simulate gases with different molecular weights. In this work, nitrogen–helium and nitrogen–nitrogen mixing layers are studied with different velocities. The computed results are compared with published experimental results and there is agreement between them within 7% for most cases.

Diffusion equations are derived for an isothermal lattice Boltzmann model with two components. The first-order upwind finite difference scheme is used to solve the evolution equations for the distribution functions. When using this scheme, the numerical diffusivity, which is a spurious diffusivity in addition to the physical diffusivity, is proportional to the lattice spacing and significantly exceeds the physical value of the diffusivity if the number of lattice nodes per unit length is too small. Flux limiter schemes are introduced to overcome this problem. Empirical analysis of the results of flux limiter schemes shows that the numerical diffusivity is very small and depends quadratically on the lattice spacing.

Liquid break up is an important phenomenon in many practical applications including combustion engines and paint sprays. The fundamental mechanisms which lead to this break up are not well understood. In this paper, the lattice Boltzmann method is employed to assess its potential for investigating these mechanisms. To do this, an axisymmetric, multiple relaxation time (MRT) lattice Boltzmann method, which allows for higher Reynolds numbers to be achieved than with the standard Bhatnagar-Gross-Krook (BGK) lattice Boltzmann model, is employed to simulate liquid break up. To assess the accuracy of the model, it is employed to simulate Rayleigh break up. The computational results for Rayleigh break up are compared to experimental and theoretical predictions and shown to have agreement within several percent. Then, the model is employed to carry out initial studies of transient liquid jets to investigate the influence of surface tension, injection velocity, and liquid viscosity.

A Lattice Boltzmann model for simulating micro flows has been proposed by us recently (Europhysics Letters, 67(4), 600–606 (2004)). In this paper, we will present a further theoretical and numerical validation of the model. In this regards, a theoretical analysis of the diffuse-scattering boundary condition for a simple flow is carried out and the result is consistent with the conventional slip velocity boundary condition. Numerical validation is highlighted by simulating the two-dimensional isothermal pressure-driven micro-channel flows and the thin-film gas bearing lubrication problems, and comparing the simulation results with available experimental data and analytical predictions.

A lattice version of the Fokker–Planck equation is introduced. The resulting numerical method is illustrated through the calculation of the electric conductivity of a one-dimensional charged fluid at zero and finite-temperature.

In this paper, a recent curved non-slip wall boundary treatment for isothermal Lattice Boltzmann equation (LBE) [Z. Guo, C. Zheng and B. Shi, Phys. Fluids14(6) (2002)] is extended to handle the thermal curved wall boundary for a double-population thermal lattice Boltzmann equation (TLBE). The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a first-order extrapolation from fluid lattices. To validate the thermal boundary condition treatment, we carry out numerical simulations of Couette flow between two circular cylinders, the natural convection in a square cavity, and the natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder. The results agree very well with analytical solution or available data in the literature. Our numerical results also demonstrate that the TLBE together with the present boundary scheme is of second-order accuracy.

A two-dimensional finite difference Lattice Boltzmann model for liquid-vapour systems is introduced. Phase separation is achieved using the dimensionless van der Waals equation of state. A force term is added to account for the surface tension. Flux limiters and TVD schemes are used to improve the accuracy of this model.

We present a new boundary condition in the lattice Boltzmann method to model slip flow along curved boundaries. A requirement is formulated for the distribution functions based on the tunable momentum balance at the walls, which is shown to be equivalent to the constraint on the second moment. Numerical simulation of plane Couette flow in inclined channels and cylindrical Couette flow shows excellent agreement with the analytical results in the nearly continuum regime. Orientation effects on the velocity field are completely avoided.

The theory of the lattice Boltzmann automaton is based on a moment transform which is not Galilean invariant. It is explained how the central moments transform, used in the cascaded lattice Boltzmann method, overcomes this problem by choosing the center of mass coordinate system as the frame of reference. Galilean invariance is restored and the form of the kinetic theory is unaffected. Conservation laws are not compromised by the high order polyinomials in the equilibrium distribution arising from the central moment transform.

Two sources of instabilities in lattice Boltzmann simulations are discussed: negative numerical viscosity due to insufficient Galilean invariance and aliasing. The cascaded lattice Boltzmann automaton overcomes both problems. It is discussed why aliasing is unavoidable in lattice Boltzmann methods that rely on a single relaxation time. An appendix lists the complete scattering operator of the D2Q9 cascaded lattice Boltzmann automaton.

The interacting factors relating to thrombogenesis were defined by Virchow in 1856 to be abnormalities of blood chemistry, the vessel wall and haemodynamics. Together, these factors are known as Virchow's triad. Many attempts have been made to simulate numerically certain aspects of the complex phenomena of thrombosis, but a comprehensive model, which includes the biochemical and physical aspects of Virchow's triad, and is capable of predicting thrombus development within physiological geometries has not yet been developed. Such a model would consider the role of platelets and the coagulation cascade along with the properties of the flow in the chosen vessel.

A lattice Boltzmann thrombosis framework has been developed, on top of an existing flow solver, to model the formation of thrombi resulting from platelet activation and initiation of the coagulation cascade by one or more of the strands of Virchow's triad. Both processes then act in parallel, to restore homeostasis as the deposited thrombus disturbs the flow. Results are presented in a model of deep vein thrombosis (DVT), resulting from hypoxia and associated endothelial damage.

In this paper, the effects of surface wettability and topography on a droplet, which is driven by a body force to pass through grooved walls, are studied by using the multiphase lattice Boltzmann model. At small scale, the shape and velocity of the droplet were found to be strongly affected by the wettability and configuration of the wall. The drag on the droplet moving over grooved surfaces was found to decrease as the wall hydrophobicity increases. It was also found that the wettability decides whether the droplet fills or does not fill the whole grooves.

Lattice Boltzmann (LB) models for ideal gases retrieve the Navier-Stokes equation in the incompressible limit. Nevertheless, the high values of the isothermal compressibility introduce serious drawbacks. In the simulation of liquid flows through porous media, the high pressure gradients through throats and tortuous paths produce significant errors when conventional LB models are used, especially when the interest is the transient flow. In this work a significant reduction of the isothermal compressibility is reached by adjusting the equilibrium distribution moments to those obtained imposing a van der Waals pressure-density dependence and adopting a lattice with a high number of speeds. Simulation results for the shock tube problem, the velocity step problem and the transient pressure response in a tortuous channel are presented and compared with available analytical results.

The entropic lattice Boltzmann (LB) method has recently been extended to include energy conservation in order to simulate weakly compressible flows. One of the limitations of this method when using the BGK collision model is the fixed Prandtl number. In this paper a new simple method is proposed and validated in order to simulate fluids of arbitrary Prandtl number.