scholarly journals Extended Lattice Boltzmann Model

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 475
Author(s):  
Mohammad Hossein Saadat ◽  
Benedikt Dorschner ◽  
Ilya Karlin
Keyword(s):  
Flow Velocity ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Lattice Boltzmann Model ◽  
Benchmark Problems ◽  
Extended Model ◽  
Flow Gradients ◽  
Lattice Boltzmann Models

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

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.

scholarly journals An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models

1998 ◽  
Vol 09 (08) ◽  
pp. 1393-1404 ◽  
Author(s):  
D. J. Holdych ◽  
D. Rovas ◽  
J. G. Georgiadis ◽  
R. O. Buckius
Keyword(s):  
Multiphase Flow ◽  
Stress Tensor ◽  
Lattice Boltzmann ◽  
Effective Field ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Physical Parameters ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Definition Of

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

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.

Simulating anisotropic flows with isotropic lattice models via coordinate and velocity transformation

2019 ◽  
Vol 30 (10) ◽  
pp. 1941001
Author(s):  
Zimeng Wang ◽  
Junfeng Zhang
Keyword(s):  
Lattice Boltzmann ◽  
Lattice Models ◽  
Lattice Boltzmann Model ◽  
Square Lattice ◽  
Rectangular Lattice ◽  
Simulation Accuracy ◽  
Velocity Transformation ◽  
Particle Array ◽  
Lattice Boltzmann Models ◽  
Wavy Channels

We propose a rectangular lattice Boltzmann model for anisotropic flows based on coordinate and velocity transformation. Unlike other existing rectangular models which tuned the lattice Boltzmann algorithm to fit the rectangular or cuboid lattice grids, here we apply the general lattice Boltzmann method to solve the transformed system over regular square lattice grids. The method is tested with simulations of representative anisotropic flows, including flows in narrow straight and wavy channels, the Taylor–Green vortex flow, and the flow through an elliptical particle array. These simulations show that in general our method produces satisfactory results; however, the aspect ratio [Formula: see text] is limited to relatively large values ([Formula: see text]). The effects of [Formula: see text] on simulation accuracy and stability have been carefully examined, and a possible remedy to improve these concerns has been proposed. The method and analysis could be useful for future development of more robust and practical anisotropic lattice Boltzmann models for realistic simulations.

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.

Lattice Boltzmann Simulation of Effect of Rolling Manipulation of Traditional Chinese Massage on Blood Flow

2013 ◽  
Vol 275-277 ◽  
pp. 472-477
Author(s):  
Hui Li Tan ◽  
Fan Rong Kong ◽  
Ke Zhao Bai ◽  
Ling Jiang Kong
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Velocity ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Lattice Boltzmann Simulation ◽  
Simulation Based ◽  
Wall Shear ◽  
Boltzmann Method ◽  
Boltzmann Model

A 2D Lattice Boltzmann model for a blood vesssel under rolling manipulation(RM) was presented. The influence of rolling frequency and stenosis coefficient on blood flux, wall shear stress and flow velocity was given by the numerical simulation based on lattice Boltzmann method . It is found that increasing RM frequency can not always increase the flux. There is a proper RM frequency for maximum flux.When the maximum stenosis coefficient increases,the change range of flux and wall shear stress will increase. The rolling massage can also change flow velocity in different sections of blood vessel.

Transitional flows with the entropic lattice Boltzmann method

2017 ◽  
Vol 824 ◽  
pp. 388-412 ◽  
Author(s):  
B. Dorschner ◽  
S. S. Chikatamarla ◽  
I. V. Karlin
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Free Stream Turbulence ◽  
Transitional Flows ◽  
Curvature Effects ◽  
And Performance ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method ◽  
Refinement Strategy

The accuracy and performance of entropic multi-relaxation time lattice Boltzmann models are assessed for transitional flows of engineering interest. A simulation of the flow over a low-Reynolds-number$SD7003$airfoil at$Re=6\times 10^{4}$, at an angle of attack$\unicode[STIX]{x1D6FC}=4^{\circ }$, is performed and thoroughly compared to available numerical and experimental data. In order to include blockage and curvature effects, simulations of the flow in a low-pressure turbine passage composed of$T106$blade profiles, at a chord Reynolds number of$Re=6\times 10^{4}$or$Re=1.48\times 10^{5}$, for different free-stream turbulence intensities are presented. Using a multi-domain grid refinement strategy in combination with Grad’s boundary conditions yields good agreement for all simulations. The results demonstrate that the entropic lattice Boltzmann model is a viable, parameter-free alternative to modelling approaches such as large-eddy simulations with similar resolution requirements.

Lattice Boltzmann Models with Underlying Boolean Microdynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Kinetic Theory ◽  
Lattice Boltzmann ◽  
Degrees Of Freedom ◽  
Time History ◽  
Lattice Boltzmann Model ◽  
Occupation Numbers ◽  
History Of ◽  
Lattice Boltzmann Models ◽  
Boltzmann Model ◽  
Statistical Noise

This chapter takes a walk into the Jurassics of LBE, namely the earliest Lattice Boltzmann model that grew up out in response to the main drawbacks of the underlying LGCA. The earliest LBE was first proposed by G. McNamara and G. Zanetti in 1988, with the explicit intent of sidestepping the statistical noise problem plaguing its LGCA ancestor. The basic idea is simple: just replace the Boolean occupation Numbers with the corresponding ensemble-averaged population. The change in perspective is exactly the same as in Continuum Kinetic Theory (CKT); instead of tracking single Boolean molecules, one contents himself with the time history of a collective population representing a “cloud” of microscopic degrees of freedom.

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