Analytic solution for a higher-order lattice Boltzmann method: Slip velocity and Knudsen layer

2008 ◽  
Vol 78 (1) ◽  
Author(s):  
Seung Hyun Kim ◽  
Heinz Pitsch
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Analytic Solution ◽  
Higher Order ◽  
Knudsen Layer ◽  
Boltzmann Method

Is the Lattice Boltzmann Method Applicable to Rarefied Gas Flows? Comprehensive Evaluation of the Higher-Order Models

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Minoru Watari
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Higher Order ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Slip Flow Regime ◽  
Boltzmann Method ◽  
Higher Order Models

Lattice Boltzmann method (LBM) whose equilibrium distribution function contains higher-order terms is called higher-order LBM. It is expected that nonequilibrium physics beyond the Navier–Stokes can be accurately captured using the higher-order LBM. Relationship between the level of higher-order and the simulation accuracy of rarefied gas flows is studied. Theoretical basis for constructing higher-order LBM is presented. On this basis, specific higher-order models are constructed. To confirm that the models have been correctly constructed, verification simulations are performed focusing on the continuum regime: sound wave and supersonic flow in Laval nozzle. With applications to microelectromechanical systems (MEMS) in mind, low Mach number flows are studied. Shear flow and heat conduction between parallel walls in the slip flow regime are investigated to confirm the relaxation process in the Knudsen layer. Problems between concentric cylinders are investigated from the slip flow regime to the free molecule regime to confirm the effect of boundary curvature. The accuracy is discussed comparing the simulation results with pioneers' studies. Models of the fourth-order give sufficient accuracy even for highly rarefied gas flows. Increase of the particle directions is necessary as the Knudsen number increases.

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).

LATTICE BOLTZMANN METHOD FOR SIMULATING GAS FLOW IN MICROCHANNELS

2004 ◽  
Vol 15 (02) ◽  
pp. 335-347 ◽  
Author(s):  
G. H. TANG ◽  
W. Q. TAO ◽  
Y. L. HE
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Gas Flow ◽  
Specular Reflection ◽  
Gas Flows ◽  
Friction Factors ◽  
Isothermal Gas ◽  
Boltzmann Method ◽  
Good Agreement

Isothermal gas flows in microchannels is studied using the lattice Boltzmann method. A novel equation relating Knudsen number with relaxation time is derived. The slip-velocity on the solid boundaries is reasonably realized by combining the bounce-back reflection with specular reflection in a certain proportion. Predicted characteristics in a two-dimensional microchannel flow, including slip-velocity, nonlinear pressure drop, friction factors, velocity distribution along the streamwise direction and mass flow rate, are compared with available analytical and experimental results and good agreement is achieved.

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