# Interdisciplinary Applied Mathematics

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Number of buffer cells used: An additional optimization that can be implemented for DSMC/Navier-Stokes coupling is to use two rows of buffer cells instead    of    one.    Using two    or    more    rows    of buffer    cells    makes certain

that the buffer region has enough depth to inject a proper number of high-velocity particles. Furthermore, as compared to using one big buffer cell, this approach helps capture some of the gradient in the buffer zone.

Problems induced by noise in the DSMC estimates: In some cases, the noise in DSMC estimates can result in wiggles in the Navier-Stokes solution. The wiggles die off further into the continuum domain. However, the presence of wiggles may cause problems with interpolation because wrong values    may    be    interpolated.    In    order to    help    avoid    problems,    the

flexibility provided by meshless interpolation can be utilized by adjusting the cloud sizes to filter out the effect of the wiggles in the Navier-Stokes solution.

Analysis of Peclet and local Kn numbers: The Peclet number, Reynolds number, and local Kn of the flow in the interface zone can be calculated to provide information on the characteristics of the filter problem. An analysis of the Peclet number shows that in the Navier-Stokes subdomains, the local Peclet number, defined by using point-to-point spacing, is smaller than or close to 1.    The    Peclet    number is highest    at    the    regions    closest    to    the

input and output of the channels. In the simulations described here, numerical stabilization    is    not    used.    However,    for    larger    values    of    Peclet    number

stabilization will    be necessary.    An    analysis    of the    local    Kn    shows    that    a

local Kn between 0.4 p,m and 2 p,m from the channel exit is in the slip flow regime. Far from the channel exit, the global Kn is 0.011, which is at the boundary of continuum and slip flow regimes. The use of no-slip boundary conditions close to the DSMC/NS boundary may introduce some error to the coupled solution. Since the slip velocity observed from the DSMC simulation is small with respect to the maximum velocity, the error is expected to be small. The Reynolds number of the flow for the conditions studied is about 4.5. Thus, it is seen that the flow in the filter is compressible, and the use of Navier-Stokes equations is necessary in order to bring the coupling interface close to the filter channel.

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