# Interdisciplinary Applied Mathematics

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 Surface Pressure ж-velocity y-velocity temperature A 1.3 atm — 0 300 К В 1.0 atm — 0 300 К С, E dP/dy = 0 0 dvy/ду = 0 dt/dy = 0 D, F dP/dy = 0 0 dvy/ду = 0 dt/dy = 0 Si, So — vx= DSMC est. vy = DSMC est. t = DSMC est. Di, Do p = NS sol vx= NS sol. vy= NS sol. vy= NS sol. G, H — diffusive diffusive 300 к

Distribution function used for DSMC boundary cells: Previous work on DSMC coupling is not conclusive about the distribution function used for injection into the DSMC domain. It was first suggested that Chapman-Enskog distribution be used whenever DSMC is being coupled to Navier-Stokes equations (Hash and Hassan, 1996). However, it was later suggested that Chapman-Enskog distribution may not be necessary in all cases (Hash and Hassan, 1997). In (Garcia et al., 1999), a dimensionless parameter B is used to analyze the validity range of the Chapman-Enskog distribution. For the examples discussed here, the dimensionless parameter B is 0.04, which is smaller than the maximum value for the range of validity of the Chapman-Enskog distribution, which indicates that the Chapman-

Enskog distribution can be utilized. For the example presented here, the Chapman-Enskog distribution was used for the particles generated in the buffer cells. Chapman-Enskog distribution was selected because Kn at the interface was in the slip flow regime, indicating the presence of nonequilibrium. The parameters that are needed for the Chapmann-Enskog distribution were taken from the Navier-Stokes simulation of the continuum subdomain and interpolated back to the DSMC subdomain.

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