Interdisciplinary Applied Mathematics

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3.0897


0.07


2.1655


2.4259


2.5706


2.7270


2.8967


0.09


2.0698


2.3163


2.4532


2.6011


2.7618


0.1


2.0314


2.2723


2.4060


2.5507


2.7077


2.7860


4.3628


0.3


1.7092


1.8937


2.0011


2.1176


2.2448


0.5


1.6017


1.7776


1.8766


1.9844


2.1023


2.2128


3.4748


0.7


1.5591


1.7272


1.8220


1.9254


2.0388


0.8


1.5482


1.7052


1.7976


1.8986


2.0092


0.9


1.5416


2.1269


3.3392


1.0


1.5389


1.7005


1.7921


1.8921


2.0019


2.1204


3.3270

a Solutions of BGK model equation. b Solutions of Boltzmann equation.


corresponds to    BGK    solutions    of (Cercignani    et    al.,    1994),    while    the    hy


brid specular-diffuse scattering cases correspond to solutions of BGK model equation by (Loyalka, 1975) and solutions of the full Boltzmann equation by (Loyalka and Hickey, 1991).


The good approximation of solutions to Boltzmann’s equation by the


TABLE 15.4. Pressure-driven flow in a channel: Normalized flowrate Mc vs. S (rarefaction parameter) and av (accommodation coefficient) (1 < S < 10).


Mc


Loyalka (1975)a


Loyalka and Hickey (1991)b


6


a = 1


(7 = 0.92


(7 = 0.88


(7 = 0.84


(7 = 0.80


cr = 0.75


a = 0.50

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