ON THE SYSTEM SIZE OF LATTICE BOLTZMANN SIMULATIONS

2004 ◽  
Vol 15 (08) ◽  
pp. 1049-1060 ◽  
Author(s):  
GUSZTÁV MAYER ◽  
GÁBOR HÁZI ◽  
JÓZSEF PÁLES ◽  
ATTILA R. IMRE ◽  
BJÖRN FISCHER ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Lattice Site ◽  
Finite Lattice ◽  
Continuous Distribution ◽  
System Size ◽  
Dynamics Simulation ◽  
Lattice Boltzmann Simulations ◽  
Initial Assumption ◽  
Boltzmann Method ◽  
Number Of Particles

In lattice Boltzmann simulations particle groups — represented by scalar velocity distributions — are moved on a finite lattice. The size of these particle groups is not well-defined although it is crucial to assume that they should be big enough for using a continuous distribution. Here we propose to use the liquid–vapor interface as an internal yardstick to scale the system. Comparison with existing experimental data and with molecular dynamics simulation of Lennard–Jones-argon shows that the number of atoms located on one lattice site is in the order of few atoms. This contradicts the initial assumption concerning the number of particles in the group, therefore seems to raise some doubts about the applicability of the lattice Boltzmann method in certain problems whenever interfaces play important role and ergodicity does not hold.

LATTICE-BOLTZMANN SIMULATIONS OF FLOW THROUGH NAFION POLYMER MEMBRANES

2003 ◽  
Vol 17 (01n02) ◽  
pp. 135-138 ◽  
Author(s):  
HIDEMITSU HAYASHI ◽  
SATORU YAMAMOTO ◽  
SHI-AKI HYODO
Keyword(s):  
Lattice Boltzmann ◽  
Dissipative Particle Dynamics ◽  
Three Dimensional ◽  
Polymer Membranes ◽  
Dynamics Simulation ◽  
Fluid Viscosity ◽  
Lattice Boltzmann Simulations ◽  
Flow Through ◽  
Boltzmann Method ◽  
Dissipative Particle Dynamics Simulation

Simulations of flow through three-dimensional porous structures of NAFION polymer membranes are performed with a Lattice-Boltzmann method (LBM) for incompressible fluid. Geometry data of NAFION are constructed from a result of a dissipative particle dynamics simulation for three values of the water content, 10%, 20%, and 30%, and are used as the geometry input for the LBM. Permeability of the porous structure is extracted from results of the LBM simulation using Darcy's low. The permeability K is shown to be expressed as K = L2 × Ktpl with a characteristic length L and the dimensionless permeability Ktpl depending only on the topological structure of the porous media. Dependence of Ktpl is examined on the pressure gradient, the fluid viscosity, and the resolution of the computational grid.

Lattice Boltzmann Simulations for Thermal Conductivity Estimation in Heterogeneous Materials

2009 ◽  
Vol 283-286 ◽  
pp. 364-369 ◽  
Author(s):  
M.R. Arab ◽  
Bernard Pateyron ◽  
Mohammed El Ganaoui ◽  
Nicolas Calvé
Keyword(s):  
Thermal Conductivity ◽  
Porous Medium ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Theoretical Models ◽  
Short Description ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method

For simulating flows in a porous medium, a numerical tool based on the Lattice Boltzmann Method (LBM) is developed with regards to the classical D2Q9 model. A short description of this model is presented. This technique, applied to two-dimensional configurations, indicates its ability to simulate phenomena of heat and mass transfer. The numerical study is extended to estimate physical parameters that characterize porous materials, like the so-called Effective Thermal Conductivity (ETC) which is of our interest in this paper. Obtained results are compared with those which could be found analytically and by theoretical models. Finally, a porous medium is considered to find its ETC.

Numerical Simulation of Surface Roughness Effects in Laminar Lubrication Using the Lattice-Boltzmann Method

2007 ◽  
Vol 129 (3) ◽  
pp. 603-610 ◽  
Author(s):  
Gunther Brenner ◽  
Ahmad Al-Zoubi ◽  
Merim Mukinovic ◽  
Hubert Schwarze ◽  
Stefan Swoboda
Keyword(s):  
Velocity Field ◽  
Surface Texture ◽  
Lattice Boltzmann ◽  
Load Capacity ◽  
Three Dimensional ◽  
Hydrodynamic Characteristics ◽  
Real Surface ◽  
Roughness Effects ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method

The effect of surface texture and roughness on shear and pressure forces in tribological applications in the lubrication regime is analyzed by means of lattice-Boltzmann simulations that take the geometry of real surface elements into account. Topographic data on representative surface structures are obtained with high spatial resolution with the application of an optical interference technique. The three-dimensional velocity field past these surfaces is computed for laminar flow of Newtonian fluids in the continuum regime. Subsequently, pressure and shear flow factors are obtained by evaluating the velocity field in accordance with the extended Reynolds equation of Patir and Cheng (1978, ASME J. Tribol., 100, pp. 12–17). The approach allows an efficient determination of the hydrodynamic characteristics of microstructured surfaces in lubrication. Especially, the influence of anisotropy of surface texture on the hydrodynamic load capacity and friction is determined. The numerical method used in the present work is verified for a simplified model configuration, the flow past a channel with sinusoidal walls. The results obtained indicate that full numerical simulations should be used to accurately and efficiently compute the characteristic properties of film flows past rough surfaces and may therefore contribute to a better understanding and prediction of tribological problems.

LATTICE BOLTZMANN SIMULATIONS OF DROP–DROP INTERACTIONS IN TWO-PHASE FLOWS

2005 ◽  
Vol 16 (01) ◽  
pp. 25-44 ◽  
Author(s):  
KANNAN N. PREMNATH ◽  
JOHN ABRAHAM
Keyword(s):  
Shear Flow ◽  
Lattice Boltzmann ◽  
Flow Model ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Drop Deformation ◽  
Simple Shear Flow ◽  
Two Phase ◽  
Lattice Boltzmann Simulations ◽  
Boltzmann Method

In this paper, three-dimensional computations of drop–drop interactions using the lattice Boltzmann method (LBM) are reported. The LBM multiphase flow model employed is evaluated for single drop problems and binary drop interactions. These include the verification of Laplace–Young relation for static drops, drop oscillations, and drop deformation and breakup in simple shear flow. The results are compared with experimental data, analytical solutions and numerical solutions based on other computational methods, as applicable. Satisfactory agreement is shown. Initial studies of drop–drop interactions involving the head-on collisions of drops in quiescent medium and off-center collision of drops in the presence of ambient shear flow are considered. As expected, coalescence outcome is observed for the range of parameters studied.

scholarly journals Microflow Simulations via the Lattice Boltzmann Method

2011 ◽  
Vol 9 (5) ◽  
pp. 1128-1136 ◽  
Author(s):  
Nikolaos Prasianakis ◽  
Santosh Ansumali
Keyword(s):  
Exact Solution ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Order Of Convergence ◽  
Kinetic Equations ◽  
Closed Form Solutions ◽  
Lattice Boltzmann Simulations ◽  
Simulation Results ◽  
Boltzmann Method ◽  
Stationary Planar

AbstractThe exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was presented by S. Ansumali et al. [Phys. Rev. Lett., 98 (2007), 124502]. In this paper, simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments. The order of convergence to the exact solution is also studied. The lattice Boltzmann simulations are in excellent agreement with the exact solution.

scholarly journals Two-dimensional plastic flow of foams and emulsions in a channel: experiments and lattice Boltzmann simulations

2015 ◽  
Vol 766 ◽  
pp. 556-589 ◽  
Author(s):  
B. Dollet ◽  
A. Scagliarini ◽  
M. Sbragaglia
Keyword(s):  
Lattice Boltzmann ◽  
Velocity Profiles ◽  
Wall Friction ◽  
Spatial Correlations ◽  
Measured Velocity ◽  
Lattice Boltzmann Simulations ◽  
Glassy Systems ◽  
Local Shear ◽  
Glassy Materials ◽  
Boltzmann Method

AbstractIn order to understand the flow profiles of complex fluids, a crucial issue concerns the emergence of spatial correlations among plastic rearrangements exhibiting cooperativity flow behaviour at the macroscopic level. In this paper, the rate of plastic events in a Poiseuille flow is experimentally measured on a confined foam in a Hele-Shaw geometry. The correlation with independently measured velocity profiles is quantified by looking at the relationship between the localisation length of the velocity profiles and the localisation length of the spatial distribution of plastic events. To complement the cooperativity mechanisms studied in foam with those of other soft glassy systems, we compare the experiments with simulations of dense emulsions based on the lattice Boltzmann method, which are performed both with and without wall friction. Finally, unprecedented results on the distribution of the orientation of plastic events show that there is a non-trivial correlation with the underlying local shear strain. These features, not previously reported for a confined foam, lend further support to the idea that cooperativity mechanisms, originally invoked for concentrated emulsions (Goyon et al., Nature, vol. 454, 2008, pp. 84–87), have parallels in the behaviour of other soft glassy materials.

scholarly journals Lattice Boltzmann simulations of drying suspensions of soft particles

2021 ◽  
Vol 379 (2208) ◽  
pp. 20200399 ◽  
Author(s):  
M. Wouters ◽  
O. Aouane ◽  
M. Sega ◽  
J. Harting
Keyword(s):  
Lattice Boltzmann ◽  
Colloidal Suspension ◽  
Dynamics Simulation ◽  
Drying Process ◽  
Rigid Particles ◽  
Lattice Boltzmann Simulations ◽  
Soft Particles ◽  
Formation Of Cracks ◽  
Small Clusters

The ordering of particles in the drying process of a colloidal suspension is crucial in determining the properties of the resulting film. For example, microscopic inhomogeneities can lead to the formation of cracks and defects that can deteriorate the quality of the film considerably. This type of problem is inherently multiscale and here we study it numerically, using our recently developed method for the simulation of soft polymeric capsules in multicomponent fluids. We focus on the effect of the particle softness on the film microstructure during the drying phase and how it relates to the formation of defects. We quantify the order of the particles by measuring both the Voronoi entropy and the isotropic order parameter. Surprisingly, both observables exhibit a non-monotonic behaviour when the softness of the particles is increased. We further investigate the correlation between the interparticle interaction and the change in the microstructure during the evaporation phase. We observe that the rigid particles form chain-like structures that tend to scatter into small clusters when the particle softness is increased. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

scholarly journals A unified lattice Boltzmann model and application to multiphase flows

2021 ◽  
Vol 379 (2208) ◽  
pp. 20200397 ◽  
Author(s):  
Kai H. Luo ◽  
Linlin Fei ◽  
Geng Wang
Keyword(s):  
Lattice Boltzmann ◽  
Model Comparison ◽  
Collision Operator ◽  
Central Moment ◽  
Lattice Boltzmann Model ◽  
Dynamics Simulation ◽  
Flow Problems ◽  
Multiple Relaxation Time ◽  
Boltzmann Method ◽  
Boltzmann Model

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar–Gross–Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

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