Interdisciplinary Applied Mathematics

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Remark: In this book Kn =0 is commonly used to indicate the no-slip flow limit, and hence in the rest of this work Kn = 0 indicates a limit that Kn ^ 0, but never Kn = 0!


The first-order solution in Kn yields the Navier-Stokes equations, and the second-order solution in Kn yields the Burnett equations. The Woods equations have a different form in the high-order corrections of the stress tensor and heat flux terms (Woods, 1993; Welder et al., 1993).


We rewrite here equations (2.4b), (2.4c) for compressible flows in two dimensions:


d


dt


(p


(


pui



pui


+


d


pu2 + p + a ii


PU2


dxi


puu2 + ai2


E J


(E + p +


aii)u1 + a12


• u2


+ qi J


d


/


pu,2



+


puiu2 + a2i



0, (2.16)


dx2


pu2 + p + a22


(E + p +


a22)u2 + a21


• ui


+ q2)


two velocity components are denoted by


ub


u2 ) =


(u,


v) in the

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