Interdisciplinary Applied Mathematics

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surfaces becomes submicron should the DSMC method be employed. Similarly, in microchannel flows mixed slip-transition flows could occur. Hence, it is necessary to implement multidomain DSMC/continuum solvers. Depending on    the    application,    hybrid    Euler/DSMC    (Roveda    et    al.,    1998)    or

DSMC/Navier-Stokes algorithms (Hash and Hassan, 1997) can be used. Such hybrid methods require compatible kinetic-split fluxes for the Navier-Stokes portion of the scheme (Lou et al., 1998) so that an efficient coupling can be achieved. An adaptive mesh and algorithm refinement (AMAR) procedure, which embeds a DSMC-based particle method within a continuum grid, has been developed in (Garcia et al., 1999); it enables molecular-based treatments even within a continuum region. Hence, the AMAR procedure can be used to deliver microscopic and macroscopic information within the same flow region. An effective coupling approach is based on the DSMC-IP technique presented earlier in this chapter. The original idea for introducing the IP method was to reduce the high level of statistical fluctuations found in DSMC calculations. This same property makes it suitable as an interface for communicating information to large scales described by continuum-based approximations (Sun et al., 2004).

To make these ideas more concrete we discuss some possible algorithms. We assume that in the highly rarefied region (Kn > 0.1) we employ a DSMC discretization that is computationally efficient in this regime. As Kn ^ 0 the DSMC approach becomes increasingly inefficient, and thus the need for a continuum description in the low Kn region. Such a situation, for example, arises in gas flow through a long narrow tube or slit where the pressure drop downstream produces a high degree of rarefaction. The same is true for the expansion region of micronozzle flows we studied in Section 6.6.

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