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.

Comparison of existing and extended boundary conditions for the simulation of rarefied gas flows using the Lattice Boltzmann method

2020 ◽  
Vol 31 (05) ◽  
pp. 2050070 ◽  
Author(s):  
Jean-Michel Tucny ◽  
David Vidal ◽  
Sébastien Leclaire ◽  
François Bertrand
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Flow Simulation ◽  
Complex Geometries ◽  
Rarefied Flow ◽  
Rarefied Flows ◽  
Rarefied Gas Flows ◽  
Boltzmann Method

Accurate imposition of boundary conditions (BCs) is of critical importance in fluid flow computation. This is especially true for the Lattice Boltzmann method (LBM), where BC imposition is done through operations on populations rather than directly on macroscopic variables. While the regular Cartesian structure of the lattices is an advantage for flow simulation through complex geometries such as porous media, imposition of correct BCs remains a topic of investigation for rarefied flows, where slip BCs need to be imposed. In this work, current kinetic BCs from the literature are reviewed for rarefied flows and an extended version of a technique that combines bounce-back and diffusive reflection (DBB BC) is proposed to solve such flows that exhibit effective viscosity gradients. The extended DBB BC is completely local and addresses ambiguities as regards to the definition of boundary populations in complex geometries. Numerical tests of a rarefied flow through a slit were performed, confirming the intrinsic second-order convergence of the proposed extended DBB BC. It settles a long-standing debate regarding the convergence of BCs in rarefied flows. Good agreement was also found with existing numerical schemes and experimental data.

Simulation of copper–water nanofluid in a microchannel in slip flow regime using the lattice Boltzmann method

2015 ◽  
Vol 49 ◽  
pp. 89-99 ◽  
Author(s):  
Arash Karimipour ◽  
Alireza Hossein Nezhad ◽  
Annunziata D’Orazio ◽  
Mohammad Hemmat Esfe ◽  
Mohammad Reza Safaei ◽  
...  
Keyword(s):  
Lattice Boltzmann Method ◽  
Flow Regime ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Copper Water ◽  
Slip Flow Regime ◽  
Boltzmann Method

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.

A Micro-Channel Flow and Heat Transfer Study by Lattice Boltzmann Method

2003 ◽  
Author(s):  
Ru Yang ◽  
Chin-Sheng Wang
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann Method ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Navier Stokes ◽  
Micro Channel ◽  
Parallel Plates ◽  
Boltzmann Method ◽  
Good Agreement

A Lattice Boltzmann method is employed to investigate the flow characteristics and the heat transfer phenomenon between two parallel plates separated by a micro-gap. A nine-velocity model and an internal energy distribution model are used to obtain the mass, momentum and temperature distributions. It is shown that for small Knudsen numbers (Kn), the current results are in good agreement with those obtained from the traditional Navier-Stokes equation with non-slip boundary conditions. As the value of Kn is increased, it is found that the non-slip condition may no longer be valid at the wall boundary and that the flow behavior changes to one of slip-flow. In slip flow regime, the present results is still in good agreement with slip-flow solution by Navier Stokes equations. The non-linear nature of the pressure and friction distribution for micro-channel flow is gieven. Finally, the current investigation presents a prediction of the temperature distribution for micro-channel flow under the imposed conditions of an isothermal boundary.

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