Interdisciplinary Applied Mathematics

Скачать в pdf «Interdisciplinary Applied Mathematics»


In the following we present an application of the entropic LBM. Specifically, the slip boundary condition is examined for a simple setup, where


18


16


14


12


10


8


6


4


2


0




“1-1-1


-1-1


Vs +



Mf x


X




.X'»»


XX……..*


-1_1_1—1—


,v—X’


_I_


_1_1_



0    0.1    0.2    0.3    0.4    0.5    0.6    0.7    0.8


K„


FIGURE 15.21. Slip velocity and normalized mass flowrate at theThe lines correspond to equations described in the text. (Courtesy of X. Nie, G.D. Doolen, and S. Chen.)

Y


FIGURE 15.22. Velocity profile in a 2-D body force driven Poiseuille flow at Kn = 0.035 and Ma = 0.01. Comparison between the analytical solution of the BGK equation and a simulation of the entropic lattice Boltzmann method with the diffusive boundary condition. (Courtesy of I.V. Karlin and S. Ansumali.)


asymptotic analysis of the continuous Boltzmann BGK equation is possible, using the assumption of the isothermal condition. In Figure 15.22 we compare the analytical solution (Cercignani, 1975) with the simulation using the isothermal entropic lattice Boltzmann model (Karlin et al., 1999; Ansumali et al., 2003) and the diffusive boundary condition we presented earlier (Ansumali and Karlin, 2002). Good agreement is obtained for this benchmark problem without the use of any adjusted parameters. Another application of entropic LBM is presented in Section 5.4.2, where the as-


sumption of isothermal conditions is relaxed and temperature variations across the microchannel are allowed. DSMC simulations for this case reported in (Zheng et al., 2002), show that the assumption of the isothermal flow is not valid. The quasi-continuum approaches, e.g., the Navier-Stokes-Fourier description    based    on    the    slip    boundary    conditions    or    Burnett    de

Скачать в pdf «Interdisciplinary Applied Mathematics»

Метки