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.

Modeling of collapsing cavitation bubble near solid wall by 3D pseudopotential multi-relaxation-time lattice Boltzmann method

2017 ◽  
Vol 232 (3) ◽  
pp. 445-456 ◽  
Author(s):  
Minglei Shan ◽  
Yu Yang ◽  
Hao Peng ◽  
Qingbang Han ◽  
Changping Zhu
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Cavitation Bubble ◽  
Solid Wall ◽  
Three Dimensional ◽  
Lattice Boltzmann Model ◽  
Bubble Collapse ◽  
Lattice Boltzmann Simulation ◽  
Boltzmann Method ◽  
Boltzmann Model

Understanding the dynamic characteristic of the cavitation bubble near a solid wall is a fundamental issue for the bubble collapse application and prevention. In the present work, an improved three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model is adopted to investigate the cavitation bubble collapse near the solid wall. With respect to thermodynamic consistency, Laplace law verification, the three-dimensional pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. By the theoretical analysis, it is proved that the model can be regarded as a solver of the Rayleigh–Plesset equation, and confirmed by comparing the results of the lattice Boltzmann simulation and the Rayleigh–Plesset equation calculation for the case of cavitation bubble collapse in the infinite medium field. The bubble collapse near the solid wall is modeled using the improved pseudopotential multi-relaxation-time lattice Boltzmann model. We find the lattice Boltzmann simulation and the experimental results have the same dynamic process by comparing the bubble profiles evolution. Form the pressure field and the velocity field evolution it is found that the tapered higher pressure region formed near the top of the bubble is a crucial driving force inducing the bubble collapse. This exploratory research demonstrates that the lattice Boltzmann method is an alternative tool for the study of the interaction between collapsing cavitation bubble and matter.

scholarly journals Simulation of Thermomagnetic Convection in a Cavity Using the Lattice Boltzmann Model

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Mahshid Hadavand ◽  
Antonio C. M. Sousa
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann ◽  
Magnetic Force ◽  
Electrical Current ◽  
Lattice Boltzmann Model ◽  
Thermomagnetic Convection ◽  
Microelectronic Devices ◽  
Third Dimension ◽  
Boltzmann Method ◽  
Boltzmann Model

Thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension is numerically simulated using the single relaxation time lattice Boltzmann method (LBM). This problem is of considerable interest when dealing with cooling of microelectronic devices, in situations where natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid. Therefore, circulation is achieved by imposing a magnetic field, which is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection,” are analysed in terms of the flow modes and heat transfer characteristics of a magnetic fluid.

DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS

2012 ◽  
Vol 19 ◽  
pp. 90-99
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
JINSHENG CAI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
One Dimensional ◽  
Volume Method ◽  
Boltzmann Method ◽  
Boltzmann Model

In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

SIMULATING TWO- AND THREE-DIMENSIONAL MICROFLOWS BY THE LATTICE BOLTZMANN METHOD WITH KINETIC BOUNDARY CONDITIONS

2007 ◽  
Vol 18 (05) ◽  
pp. 805-817 ◽  
Author(s):  
G. H. TANG ◽  
W. Q. TAO ◽  
Y. L. HE
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Three Dimensional ◽  
Accommodation Coefficient ◽  
Lattice Boltzmann Model ◽  
Driven Cavity ◽  
Kinetic Boundary ◽  
Boltzmann Method

An entropic lattice Boltzmann model for gaseous slip flow in microchannels is presented. We relate the Knudsen number with the relaxation time in the lattice Boltzmann evolution equation from the gas kinetic theory. The slip velocity taking the momentum accommodation coefficient into account at the solid boundaries is obtained with kinetic boundary conditions. The two-dimensional micro-Poiseuille flow, microflow over a backward-facing step, micro-lid-driven cavity flow, and three-dimensional microflow are simulated using the present model. Numerical tests show that the results of the present lattice Boltzmann method together with the boundary scheme are in good agreement with the analytical solutions and numerical simulations by the finite volume method.

scholarly journals Numerical Simulation of Driven Convective Heat Transfer Based Lattice Boltzmann Method in a Porous Cavity

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
You-Sheng Xu ◽  
Rui-Min Wang ◽  
Guo-Neng Li ◽  
You-Qu Zheng
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Lattice Boltzmann Model ◽  
Published Data ◽  
Porous Cavity ◽  
Convective Thermal ◽  
Transfer Behavior ◽  
Boltzmann Method ◽  
Boltzmann Model

A lattice Boltzmann model of the uniform velocity, driven convective thermal conductivity in a porous cavity is studied. The Darcy, Richardson, and Reynolds numbers are shown to have a significant influence on the heat transfer behavior and the horizontal velocity of the flow field, while the porosity has little influence on either. The model is validated by the average Nusselt number at different Reynolds numbers, and the numerical results are in good agreement with available published data.

scholarly journals A unified lattice Boltzmann model and application to multiphase flows

2021 ◽  
Vol 379 (2208) ◽  
pp. 20200397 ◽  
Author(s):  
Kai H. Luo ◽  
Linlin Fei ◽  
Geng Wang
Keyword(s):  
Lattice Boltzmann ◽  
Model Comparison ◽  
Collision Operator ◽  
Central Moment ◽  
Lattice Boltzmann Model ◽  
Dynamics Simulation ◽  
Flow Problems ◽  
Multiple Relaxation Time ◽  
Boltzmann Method ◽  
Boltzmann Model

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar–Gross–Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

SIMULATION OF GENERALIZED NEWTONIAN FLUIDS WITH THE LATTICE BOLTZMANN METHOD

2007 ◽  
Vol 18 (12) ◽  
pp. 1939-1949 ◽  
Author(s):  
ORESTIS MALASPINAS ◽  
GUY COURBEBAISSE ◽  
MICHEL DEVILLE
Keyword(s):  
Power Law ◽  
Lattice Boltzmann ◽  
Recent Progress ◽  
Lattice Boltzmann Model ◽  
Sharp Corner ◽  
Power Law Model ◽  
Generalized Newtonian Fluid ◽  
Planar Contraction ◽  
Boltzmann Method ◽  
Boltzmann Model

This paper proposes a study of the computational efficiency of a lattice Boltzmann model (LBM) solver to simulate the behavior of a generalized Newtonian fluid. We present recent progress concerning a 4-1 planar contraction considering a power-law and a Carreau-law model. First we compare the power-law model for a Poiseuille flow with the analytical solution, and show that our model is second-order accurate in space. Then we compare the results obtained with LBM for both laws to those obtained using a commercial finite element solver for the 4-1 plane sharp corner contraction.

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.

Lattice Boltzmann Simulation of Nucleation

2003 ◽  
Author(s):  
Takeshi Seta ◽  
Kenichi Okui ◽  
Eisyun Takegoshi
Keyword(s):  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Two Phase Flows ◽  
Two Phase ◽  
Lattice Boltzmann Simulation ◽  
Expansion Procedure ◽  
Theoretical Predictions ◽  
Boltzmann Method ◽  
Boltzmann Model ◽  
Pseudo Potential

We propose a lattice Boltzmann model capable of simulating nucleation. This LBM modifies a pseudo-potential so that it recovers a full set of hydrodynamic equations for two-phase flows based on the van der Waals-Cahn-Hilliard free energy theory through the Chapman-Enskog expansion procedure. Numerical measurements of thermal conductivity and of surface tension agree well with theoretical predictions. Simulations of phase transition, nucleation, pool boiling are carried out. They demonstrate that the model is applicable to two-phase flows with thermal effects. Using finite difference Lattice Boltzmann method ensures numerical stability of the scheme.

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