Interdisciplinary Applied Mathematics

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15.3.2 Navier-Stokes/DSMC Coupling

When compared to DSMC/Stokes coupling, the application of DSMC/Nav-ier-Stokes coupling involves several issues: coupling of temperature, the presence of larger gradients at the interface and/or the overlap region, the behavior of Navier-Stokes equations in the presence of noisy boundary conditions, and the distribution function for the particles injected into the DSMC region. These and related issues are discussed below.

The coupling of the pressure and velocity is performed in the same manner as the DSMC/Stokes coupling. For the coupling of temperature, several alternatives can be implemented. Typically, coupling the temperature in the same way as velocity gives the best results. That is, the temperature estimated from DSMC is interpolated to the Navier-Stokes subdomains; and after the Navier-Stokes solution, the temperature from within the continuum subdomain is interpolated back to the DSMC boundary cells. The transfer of variables between subdomains for coupling is summarized in Table 15.2 (see Figure 15.7 for the microfilter geometry). In contrast to velocity coupling, in the absence of overlap, the temperature does not converge. For this reason, the DSMC/Navier-Stokes coupling described here uses nonzero overlap.

In addition to the scheme described in Table 15.2, other possibilities for the coupling of temperature can also be implemented. However, we observed that the Navier-Stokes solution does not converge if the temperature is    not    specified    at    the    interfaces with    the    atomistic    model. Also,    it    was

observed that when the temperature at the boundary of the DSMC subdomain is updated by extrapolating the value from the neighboring cells, the method becomes unreliable, with the temperature solution differing significantly from the DSMC solution in some cases.

TABLE 15.2. A summary of boundary conditions on various surfaces of the microfilter geometry.

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