scholarly journals Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

2011 ◽  
Vol 230 (3) ◽  
pp. 835-849 ◽  
Author(s):  
Jianping Meng ◽  
Yonghao Zhang
Keyword(s):  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
High Order ◽  
Gas Flows ◽  
Accuracy Analysis ◽  
Rarefied Gas Flows ◽  
Lattice Boltzmann Models

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.

High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation

2015 ◽  
Vol 18 (4) ◽  
pp. 1012-1049 ◽  
Author(s):  
Manuel A. Diaz ◽  
Min-Hung Chen ◽  
Jaw-Yen Yang
Keyword(s):  
Rarefied Gas ◽  
Collision Operator ◽  
High Order ◽  
Gas Flows ◽  
Correction Procedure ◽  
Bgk Model ◽  
Time Step ◽  
Asymptotic Preserving ◽  
Bgk Equation ◽  
Rarefied Gas Flows

AbstractHigh-order and conservative phase space direct solvers that preserve the Euler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gas flows are explored and studied. The approach is based on the conservative discrete ordinate method for velocity space by using Gauss Hermite or Simpsons quadrature rule and conservation of macroscopic properties are enforced on the BGK collision operator. High-order asymptotic-preserving time integration is adopted and the spatial evolution is performed by high-order schemes including a finite difference weighted essentially non-oscillatory method and correction procedure via reconstruction schemes. An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equation when the correction procedure via reconstruction scheme is used. The effects of the discrete velocity conservative property and accuracy of high-order formulations of kinetic schemes based on BGK model methods are provided. Extensive comparative tests with one-dimensional and two-dimensional problems in rarefied gas flows have been carried out to validate and illustrate the schemes presented. Potentially advantageous schemes in terms of stable large time step allowed and higher-order of accuracy are suggested.

Thermal Lattice Boltzmann Simulation of Rarefied Gas Flows in Nanochannels for Wide Range of Knudsen Number

2011 ◽  
Vol 403-408 ◽  
pp. 5313-5317
Author(s):  
A.H. Meghdadi Isfahani ◽  
A. Soleimani
Keyword(s):  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Knudsen Numbers ◽  
Lattice Boltzmann Simulation ◽  
Wide Range ◽  
Flow Through ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann

Using a modified Lattice Boltzmann Method (LBM), developing thermal flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity and thermal conductivity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen numbers, Kn,. The results show that in spite of the standard LBM, the temperature distributions and the local Nusselt number obtained from this modified thermal LBM, agree well with the other numerical and empirical results in a wide range of Knudsen numbers.

scholarly journals A Thermal Lattice Boltzmann Model for Micro/Nano-Flows

2008 ◽  
Author(s):  
Y.-H. Zhang ◽  
X.-J. Gu ◽  
R. W. Barber ◽  
D. R. Emerson
Keyword(s):  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Computational Cost ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Gas Flows ◽  
Low Speed ◽  
Rarefied Gas Flows ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

With the development of micro/nano-devices, low speed rarefied gas flows have attracted significant research interest where successful numerical methods for traditional high speed flows, including the direct simulation Monte Carlo method, become computationally too expensive. As the Knudsen number can be up to the order of unity in a micro/nano flow, one approach is to use continuum-based methods including the Navier-Stokes-Fourier (NSF) equations, Burnett/super Burnett equations, and moment models. Limited success has been achieved because of theoretical difficulties and/or numerical problems. The recently developed lattice Boltzmann equation (LBE) offers a fundamentally different approach which is close to kinetic methods but with a significantly smaller computational cost. However, success of LBE methods for rarefied gas motion has been mainly on isothermal flows. In this paper, thermal rarefied gas flows are investigated. Due to the unique features of micro/nano flows, a simplified thermal lattice Boltzmann model with two distribution functions can be used. In addition, kinetic theory boundary conditions for the number density distribution function can be extended to construct a thermal boundary condition. The model has been validated in the slip-flow regime against solutions of the NSF equations for shear and pressure driven flows between two planar plates. It is shown that the present thermal LBE model can capture some unique flow characteristics that the NSF equations fail to predict. The present work indicates that the thermal lattice Boltzmann model is a computationally economic method that is particularly suitable to simulate low speed thermal rarefied gas flows.

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