DIFFUSIVITY OF TWO-COMPONENT ISOTHERMAL FINITE DIFFERENCE LATTICE BOLTZMANN MODELS

2005 ◽  
Vol 16 (07) ◽  
pp. 1075-1090 ◽  
Author(s):  
VICTOR SOFONEA ◽  
ROBERT F. SEKERKA
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Lattice Spacing ◽  
Evolution Equations ◽  
Unit Length ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Flux Limiter ◽  
Lattice Boltzmann Models ◽  
Boltzmann Model

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.

scholarly journals Improved phase-field-based lattice Boltzmann models with a filtered collision operator

2019 ◽  
Vol 30 (10) ◽  
pp. 1941009
Author(s):  
Hiroshi Otomo ◽  
Raoyang Zhang ◽  
Hudong Chen
Keyword(s):  
Phase Field ◽  
Lattice Boltzmann ◽  
Density Ratio ◽  
Collision Operator ◽  
Analytic Solutions ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Low Viscosity ◽  
Lattice Boltzmann Models ◽  
Boltzmann Model

In this study, a phase-field lattice Boltzmann model based on the Allen–Cahn equation with a filtered collision operator and high-order corrections in the equilibrium distribution functions is presented. Here, we show that in addition to producing numerical results consistent with prior numerical methods, analytic solutions, and experiments with the density ratio of 1000, previous numerical deficiencies are resolved. Specifically, the new model is characterized by robustness at low viscosity, accurate prediction of shear stress at interfaces, and removal of artificial dense bubbles and rarefied droplets, etc.

scholarly journals A PARALLEL THERMAL LATTICE BOLTZMANN MODEL WITH FLUX LIMITERS FOR MICROSCALE FLOW

2008 ◽  
Vol 19 (12) ◽  
pp. 1847-1861 ◽  
Author(s):  
M. BOTTI ◽  
G. GONNELLA ◽  
A. LAMURA ◽  
F. MASSAIOLI ◽  
V. SOFONEA
Keyword(s):  
Lattice Boltzmann ◽  
Evolution Equations ◽  
Parallel Implementation ◽  
Lattice Boltzmann Model ◽  
Driven Cavity ◽  
Slip Regime ◽  
Microscale Flow ◽  
Thermal Lattice Boltzmann ◽  
Flux Limiters ◽  
Boltzmann Model

We propose a thermal lattice Boltzmann model to study gaseous flow in microcavities. The model relies on the use of a finite difference scheme to solve the set of evolution equations. By adopting diffuse reflection boundary conditions to deal with flows in the slip regime, we study the micro-Couette flow in order to select the best numerical scheme in terms of accuracy. The scheme based on flux limiters is then used to simulate a micro-lid-driven cavity flow by using an efficient and parallel implementation. The numerical results are in very good agreement with the available results recovered with different methods.

scholarly journals Recovery of Galilean invariance in thermal lattice Boltzmann models for arbitrary Prandtl number

2014 ◽  
Vol 25 (10) ◽  
pp. 1450046 ◽  
Author(s):  
Hudong Chen ◽  
Pradeep Gopalakrishnan ◽  
Raoyang Zhang
Keyword(s):  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Relaxation Times ◽  
Collision Operator ◽  
Lattice Boltzmann Model ◽  
Operator Form ◽  
Prandtl Numbers ◽  
Lattice Boltzmann Models ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well-known non-Galilean invariant artifact at nonunity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times.

1308 Study of a finite difference lattice Boltzmann model considering large density difference

2004 ◽  
Vol 2004.79 (0) ◽  
pp. _13-15_-_13-16_
Author(s):  
Michihisa Tsutahara ◽  
Kazuhiko Ogawa ◽  
Masahiko Sakamoto ◽  
Hiroki Yokoyama ◽  
Masakazu Tajima ◽  
...  
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Density Difference ◽  
Lattice Boltzmann Model ◽  
Large Density ◽  
Boltzmann Model

SLIP ON CURVED BOUNDARIES IN THE LATTICE BOLTZMANN MODEL

2007 ◽  
Vol 18 (01) ◽  
pp. 15-24 ◽  
Author(s):  
LAJOS SZALMÁS
Keyword(s):  
Couette Flow ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Momentum Balance ◽  
Curved Boundaries ◽  
Cylindrical Couette Flow ◽  
Boltzmann Method ◽  
Boltzmann 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.

scholarly journals A Study of New Finite Difference Lattice Boltzmann Model.

2002 ◽  
Vol 68 (665) ◽  
pp. 15-21 ◽  
Author(s):  
Michihisa TSUTAHARA ◽  
Makoto KURITA ◽  
Takeyoshi IWAGAMI
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Boltzmann Model
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