# Interdisciplinary Applied Mathematics

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Example: The coupled DSMC/Navier-Stokes approach is applied to the microfilter geometry shown in Figure 15.7. The various geometrical param-

FIGURE 15.12. The DSMC and coupled results for temperature plotted along the    midline    for    dMc = 0.6    ym,    dov = 0.29    ym.    The    vertical    lines    denote    the

boundaries of the Navier-Stokes subdomains.

eters shown in Figure 15.7 are set to be hf = 5 ym, lc = 1 ym, = 6 ym, lout = 8 ym, and hc = 0.8 ym. Figure 15.7 also shows the decomposition of the filter geometry into Navier-Stokes and DSMC subdomains. The extension of the DSMC subdomain on each side of the channel is denoted by dext. The region simulated by DSMC on each side of the channel is denoted by dMC = dextdov. The overlap between DSMC and Navier-Stokes subdomains is denoted by dov. Again, 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. An identical overlap distance, dov, is used for both the input and the output regions. The boundary conditions imposed on various surfaces of the microfilter geometry are listed in Table 15.2.    For    all    the    simulations,    a DSMC    time    step    of    10 ps    was    used.

For the coupled DSMC/NS analysis, a total of 80 x 103 DSMC iterations were performed to make certain the coupling procedure converged, and the averages    were    collected for    at    least    2    ys.    For    the    DSMC simulations,

a transient of 1.5 ys was simulated, and averages were collected for 1 ys. The parameters of the fluid for Navier-Stokes simulation were set at the values corresponding to the DSMC values. The filter geometry shown in Figure 15.7 was simulated with the coupled method using dMC = 0.6 ym and dov = 0.29 ym. The results for temperature are compared with DSMC solution in Figure 15.12 (see (Aktas et al., 2003), for results on pressure and velocity). The good agreement between the DSMC and multiscale results demonstrates the accuracy of the coupled method.

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