Lattice Boltzmann Method For Microflows And Heat Transfer

Based on the microscale model, The lattice boltzmann method (LBM)is a novel meso-scopic method to simulation the macroscale transport phenomenon in the past decades.Compared with the traditional methods, the LBM has its merits, such as the simplicity, lo-cation, natural parallel and deal easily with the complex boundary problems, to simulate thecomplex ?ows. In recent years, the LBM has gotten important development in constructingmodels and simulating the macro?ows, but the LBM still has many problems under the mi-croscale ?ows, especially, how to determine the collection between the relaxation timeτandthe Kundsen number Kn and how to deal with the boundary conditions. For the microscale?ows, the relaxation time is vary with the local kundsen numbers. Especially, the nonslipboundary condition is never suitable for the microscale flows. Because the micro?ows haveboth velocity slips and temperature jumps under the microscale systems.This thesis is mainly proposing a simplified thermal model with the viscous dissipationterm. Compared with the Multi-speed method, present model avoid the complex equibriumdistribution, the fixed Pr number and the server numerical instability. As for the He-Luomodel, the new model can avoid the space discretion which may induce the numericalinstability. It has more flexibility, simple equibrium distribution and keeps the doubledistribution function's merits. In the numerical simulation, not only we could use D2Q4,D2Q5 models, but also use D2Q9 model. As for the viscous dissipation term, we neednot discrete the space difference, but through the distribution functions. Meanwhile, weget a second order slip boundary conditions through the Navier-Stokes equations. At thesame time, we apply the new thermal model and the second order nonslip Non-equilibriumextrapolation scheme to microscale ?ows and heat transfer. And the experiment's results ofthe thermal Couette ?ows are agree well with the analytical results.