Viscosity of finite difference lattice Boltzmann models

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.

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REDUCTION OF SPURIOUS VELOCITY IN FINITE DIFFERENCE LATTICE BOLTZMANN MODELS FOR LIQUID–VAPOR SYSTEMS

International Journal of Modern Physics C ◽

10.1142/s0129183103005388 ◽

2003 ◽

Vol 14 (09) ◽

pp. 1251-1266 ◽

Cited By ~ 43

Author(s):

ARTUR CRISTEA ◽

VICTOR SOFONEA

Keyword(s):

Finite Difference ◽

Lattice Boltzmann ◽

Evolution Equations ◽

Correction Term ◽

Interface Velocity ◽

Maxwell Construction ◽

The One ◽

Lattice Boltzmann Models ◽

Sharp Interfaces ◽

Liquid Vapor

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.

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Comparison between isothermal collision-streaming and finite-difference lattice Boltzmann models

International Journal of Modern Physics C ◽

10.1142/s0129183119410055 ◽

2019 ◽

Vol 30 (10) ◽

pp. 1941005 ◽

Cited By ~ 2

Author(s):

G. Negro ◽

S. Busuioc ◽

V. E. Ambruş ◽

G. Gonnella ◽

A. Lamura ◽

...

Keyword(s):

Shock Wave ◽

Wave Propagation ◽

Computational Complexity ◽

Finite Difference ◽

Lattice Boltzmann ◽

Shear Waves ◽

Physical Problems ◽

Benchmark Tests ◽

Simulation Results ◽

Lattice Boltzmann Models

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor–Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.

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Role of Dispersion and Optical Phonons in a Lattice-Boltzmann Finite-Difference Model for Nanoscale Thermal Conduction

International Journal for Multiscale Computational Engineering ◽

10.1615/intjmultcompeng.v6.i4.60 ◽

2008 ◽

Vol 6 (4) ◽

pp. 349-360 ◽

Cited By ~ 2

Author(s):

Pekka Heino

Keyword(s):

Finite Difference ◽

Lattice Boltzmann ◽

Thermal Conduction ◽

Optical Phonons ◽

Difference Model ◽

Finite Difference Model

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The Fluctuating Lattice Boltzmann

10.1093/oso/9780199592357.003.0030 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Brownian Motion ◽

Fluid Flow ◽

Lattice Boltzmann ◽

Thermal Fluctuations ◽

Directed Motion ◽

Statistical Fluctuations ◽

Lattice Boltzmann Models ◽

Motion Versus ◽

The Way

Fluid flow at nanoscopic scales is characterized by the dominance of thermal fluctuations (Brownian motion) versus directed motion. Thus, at variance with Lattice Boltzmann models for macroscopic flows, where statistical fluctuations had to be eliminated as a major cause of inefficiency, at the nanoscale they have to be summoned back. This Chapter illustrates the “nemesis of the fluctuations” and describe the way they have been inserted back within the LB formalism. The result is one of the most active sectors of current Lattice Boltzmann research.

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Lattice Boltzmann Models without Underlying Boolean Microdynamics

10.1093/oso/9780199592357.003.0013 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Lattice Boltzmann ◽

High Viscosity ◽

Top Down ◽

Bottom Up ◽

Low Reynolds ◽

Lattice Boltzmann Models ◽

Exponential Complexity ◽

Statistical Noise ◽

Collision Rule

Chapter 12 showed how to circumvent two major stumbling blocks of the LGCA approach: statistical noise and exponential complexity of the collision rule. Yet, the ensuing LB still remains connected to low Reynolds flows, due to the low collisionality of the underlying LGCA rules. The high-viscosity barrier was broken just a few months later, when it was realized how to devise LB models top-down, i.e., based on the macroscopic hydrodynamic target, rather than bottom-up, from underlying microdynamics. Most importantly, besides breaking the low-Reynolds barrier, the top-down approach has proven very influential for many subsequent developments of the LB method to this day.

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