Two-relaxation time lattice Boltzmann models for the ion transport equation in electrohydrodynamic flow: D2Q5 vs D2Q9 and D3Q7 vs D3Q27

2021 ◽  
Vol 33 (4) ◽  
pp. 044108
Author(s):  
Baojie Zhu ◽  
Yifei Guan ◽  
Jian Wu
Keyword(s):  
Relaxation Time ◽  
Ion Transport ◽  
Transport Equation ◽  
Lattice Boltzmann ◽  
Electrohydrodynamic Flow ◽  
Lattice Boltzmann Models

A GENERAL MULTIPLE-RELAXATION-TIME BOLTZMANN COLLISION MODEL

2007 ◽  
Vol 18 (04) ◽  
pp. 635-643 ◽  
Author(s):  
XIAOWEN SHAN ◽  
HUDONG CHEN
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Lattice Structure ◽  
Transport Coefficients ◽  
Hermite Polynomials ◽  
Simple Extension ◽  
Relaxation Rates ◽  
Collision Model ◽  
Multiple Relaxation Time ◽  
Lattice Boltzmann Models

We formulate a simple extension to the Bhatnagar-Gross-Krook collision model by expanding the distribution function in Hermite polynomials and assigning a relaxation time to each hydrodynamic moment. By discretizing the velocity space, multiple-relaxation-time lattice Boltzmann models can be constructed. The transport coefficients are analytically calculated and numerically verified. At the lowest order, allowing different relaxation rates for the second and third Hermite components results in a variable Prandtl number. Comparing with the previously proposed multiple-relaxation-time lattice Boltzmann models, the present formulation is general in the sense that it is independent of the underlying lattice structure and does not require a procedure for transformation of base vectors.

scholarly journals Derivation of Hydrodynamics for Multi-Relaxation Time Lattice Boltzmann using the Moment Approach

2013 ◽  
Vol 13 (3) ◽  
pp. 614-628 ◽  
Author(s):  
Goetz Kaehler ◽  
Alexander J. Wagner
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Collision Operator ◽  
Significant Degree ◽  
Space Representation ◽  
Peculiar Velocities ◽  
Lattice Boltzmann Simulation ◽  
Moment Approach ◽  
The Moment ◽  
Lattice Boltzmann Models

AbstractA general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without explicitly moving into a moment space representation. The corresponding ‘moments’ are derived as left eigenvectors of said collision operator in velocity space. Consequently we can, in a representation independent of the chosen base velocity set, generate the conservation equations. We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant. We explain why MRT implementations in the literature reproduce identical hydrodynamics despite being based on different orthogonalization relations. More importantly, however, we outline a minimal set of requirements on the moment base necessary to maintain the validity of the hydrodynamic equations. This is particularly useful in the context of position and time-dependent moments such as those used in the context of peculiar velocities and some implementations of fluctuations in a lattice-Boltzmann simulation.

The Fluctuating Lattice Boltzmann

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.

Lattice Boltzmann Models without Underlying Boolean Microdynamics

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.

scholarly journals Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

2019 ◽  
Vol 31 (01) ◽  
pp. 2050017
Author(s):  
Liang Wang ◽  
Xuhui Meng ◽  
Hao-Chi Wu ◽  
Tian-Hu Wang ◽  
Gui Lu
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Distance Ratio ◽  
Single Node ◽  
Convection Diffusion ◽  
Velocity Models ◽  
Discrete Effect

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

Sign in / Sign up

Export Citation Format

Share Document