Interdisciplinary Applied Mathematics

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15.3.1 Stokes/DSMC Coupling


The coupled DSMC/Stokes approach is applied to the microfilter geometry shown in Figure 15.7. The various geometrical parameters shown in Figure 15.7 are set to be hf = 5 pm, lc = 1 pm, lin = 7 pm, lout = 7 pm and hc = 0.2pm; see also (Aktas and Aluru, 2002), for results on hc = 0.8pm. Figure 15.7 also shows the decomposition of the filter geometry into Stokes and DSMC    subdomains.    The    extension    of    the    DSMC    subdomain    on    each


side of    the    channel    is denoted    by    dext. Observe    that    for    this    example,


we have one DSMC subdomain and two Stokes subdomains. In order to make sure that the flow is approximately incompressible at the interface, dext = 2 pm is used. The overlap between DSMC and Stokes subdomains is denoted by dov. The overlap is measured from the center of the DSMC estimation cells to the continuum nodes; i.e., the generation cells are not counted in the overlap because these cells do not have valid data that can be used. An identical overlap distance, dov, is used for both the input and the output regions.    The    initial    state    and    the    boundary    conditions    for    the


DSMC subdomain are selected far from the expected steady-state solution in order to test the convergence characteristics of the coupled approach. The boundary conditions imposed on various surfaces of the microfilter geometry are    listed    in    Table    15.1.    The    initial pressure    was    set    to 5.0    atm,


and the    initial    velocity    was    set to 0    m/s    for    the DSMC    subdomain.    For


all the simulations, a DSMC time step of 10 ps was used. For the coupled DSMC/Stokes analysis, a total of 50 x 103 DSMC iterations were performed to make sure the coupling procedure has converged, and the averages were collected    for    1    ps.    For    the    DSMC simulations,    a transient    of    1.5    ps    was


simulated, before the averages were collected for 1 ps.

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