Lattice Boltzmann method with regularized pre-collision distribution functions

2006 ◽  
Vol 72 (2-6) ◽  
pp. 165-168 ◽  
Author(s):  
Jonas Latt ◽  
Bastien Chopard
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Distribution Functions ◽  
Boltzmann Method

Rayleigh-Taylor Instability Studied With Multi-Relaxation Lattice Boltzmann Method

2013 ◽  
Author(s):  
Saeed J. Almalowi ◽  
Dennis E. Oztekin ◽  
Alparslan Oztekin
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Early Stage ◽  
Density Ratio ◽  
Side Wall ◽  
Immiscible Fluids ◽  
Distribution Functions ◽  
Lattice Arrangement ◽  
Boltzmann Method ◽  
Late Stages

Multi relaxation lattice Boltzmann method is implemented to study Rayleigh-Taylor instabilities. Two immiscible fluids (oil and water) are arrayed into three layers. D2Q9 lattice arrangement for two dimensional computational domains is employed. Density distribution functions for each fluid and distribution functions for the coloring step are determined. The evolution of the interface is identified with the coloring step. Buoyancy and other interaction forces, created by buoyancy, between phases are modeled. Two cases are studied one with periodic boundary condition instead of a side wall, and one bounded on all sides. The study is done with an aspect ratio of two and a density ratio of 1.2. The early and late stages of the instability are characterized. The early stage of both cases shows the initial periodic disturbance being amplified rapidly on the lower interface. The late stages show mushroom-like structures, with significant distortions occurring on the bounded case.

Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux

2019 ◽  
Vol 30 (6) ◽  
pp. 3371-3398 ◽  
Author(s):  
Masoud Mozaffari ◽  
Annunziata D’Orazio ◽  
Arash Karimipour ◽  
Ali Abdollahi ◽  
Mohammad Reza Safaei
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Convection Heat Transfer ◽  
Distribution Functions ◽  
Convection Heat ◽  
Content Type ◽  
Double Population ◽  
Boltzmann Method

Purpose The purpose of this paper is to improve the lattice Boltzmann method’s ability to simulate a microflow under constant heat flux. Design/methodology/approach Develop the thermal lattice Boltzmann method based on double population of hydrodynamic and thermal distribution functions. Findings The buoyancy forces, caused by gravity, can change the hydrodynamic properties of the flow. As a result, the gravity term was included in the Boltzmann equation as an external force, and the equations were rewritten under new conditions. Originality/value To the best of the authors’ knowledge, the current study is the first attempt to investigate mixed-convection heat transfer in an inclined microchannel in a slip flow regime.

SIMULATION OF SHOCK-WAVE PROPAGATION WITH FINITE VOLUME LATTICE BOLTZMANN METHOD

2007 ◽  
Vol 18 (04) ◽  
pp. 447-454 ◽  
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
YONG TIAN CHEW
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Distribution Functions ◽  
Shock Wave Propagation ◽  
Simple Function ◽  
Boltzmann Method

A new approach was recently proposed to construct equilibrium distribution functions [Formula: see text] of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct [Formula: see text]. In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.

scholarly journals Lattice Boltzmann Method Simulation of 3-D Melting Using Double MRT Model With Interfacial Tracking Method

2016 ◽  
Author(s):  
Zheng Li ◽  
Mo Yang ◽  
Yuwen Zhang
Keyword(s):  
Lattice Boltzmann Method ◽  
Numerical Method ◽  
Lattice Boltzmann ◽  
Liquid Fraction ◽  
Melting Process ◽  
Distribution Functions ◽  
Collision Term ◽  
Melting Front ◽  
Tracking Method ◽  
Boltzmann Method

Three-dimensional melting problems are investigated numerically with Lattice Boltzmann method (LBM). Regarding algorithm’s accuracy and stability, Multiple-Relaxation-Time (MRT) models are employed to simplify the collision term in LBM. Temperature and velocity fields are solved with double distribution functions, respectively. 3-D melting problems are solved with double MRT models for the first time in this article. The key point for the numerical simulation of a melting problem is the methods to obtain the location of the melting front and this article uses interfacial tracking method. The interfacial tracking method combines advantages of both deforming and fixed grid approaches. The location of the melting front was obtained by calculating the energy balance at the solid-liquid interface. Various 3-D conduction controlled melting problems are solved firstly to verify the numerical method. Liquid fraction tendency and temperature distribution obtained from numerical methods agree with the analytical results well. The proposed double MRT model with interfacial tracking method is valid to solve 3-D melting problems. Different 3-D convection controlled melting problems are then solved with the proposed numerical method. Various locations of the heat surface have different melting front moving velocities, due to the natural convection effects. Rayleigh number’s effects to the 3-D melting process is discussed.

Lattice Boltzmann Method for Steady Gas Flows in Microchannels With Imposed Slip Wall Boundary Condition

2007 ◽  
Author(s):  
Seckin Gokaltun ◽  
George S. Dulikravich
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Lattice Structure ◽  
Solid Wall ◽  
Distribution Functions ◽  
Gas Flows ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Boltzmann Method

In this paper, we use a lattice Boltzmann method (LBM) for simulation of rarefied gas flows in microchannels at the slip flow regime. LBM uses D2Q9 lattice structure and BGK collision operator with single relaxation time. The solid wall boundary conditions used in this paper are based on the idea of bounceback of the non-equilibrium part of particle distribution in the normal direction to the boundary. The same idea is implemented at inlet and exit boundaries as well as at the wall surfaces. The distribution functions at the solid nodes are modified according to imposed density and slip velocity values at the wall boundaries. Simulation results are presented for microscale Couette and Poiseuille flows. The results are validated against analytical and/or experimental data for the slip velocity, nonlinear pressure drop and mass flow rate at various flow conditions. It was observed that the current application of LBM can accurately recover the physics of microscale flow phenomena in microchannels. The type of boundary treatment used in this study enables the implementation of coupled simulations where the flow properties at the regions near the wall can be obtained by other numerical methods such as the Direct Simulation Monte Carlo method (DSMC).

A Simplified Lattice Boltzmann Method without Evolution of Distribution Function

2016 ◽  
Vol 9 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Z. Chen ◽  
C. Shu ◽  
Y. Wang ◽  
L. M. Yang ◽  
D. Tan
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Numerical Test ◽  
Distribution Functions ◽  
Navier Stokes ◽  
Equilibrium Distribution Function ◽  
The Difference ◽  
Boltzmann Method

AbstractIn this paper, a simplified lattice Boltzmann method (SLBM) without evolution of the distribution function is developed for simulating incompressible viscous flows. This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis. In SLBM, the equilibrium distribution function is calculated from the macroscopic variables, while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopic variables rather than the distribution function. As a result, lower virtual memories are required and physical boundary conditions could be directly implemented. Through numerical test at high Reynolds number, the method shows very nice performance in numerical stability. An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space. More benchmark tests, including the Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conducted to further validate the present method; and the simulation results are in good agreement with available data in literatures.

Sign in / Sign up

Export Citation Format

Share Document