Interdisciplinary Applied Mathematics

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usually sufficient for monatomic gases or for cases with negligible vibrational and rotational nonequilibrium effects. To demonstrate this claim we investigate the accuracy of our DSMC results in Section 4.2 by performing higher-resolution DSMC studies. The original resolution studies for microchannels employed 6,000 cells with 80,000 simulated molecules, and the results were sampled for 2.0 x 106 time steps. In Figure 15.2 comparisons of Kn = 0.1 and Kn = 2.0 channel flow velocity profiles obtained by VHS and VSS models for various cell and simulated molecule resolutions are presented. The 24,000 cells with 480,000 molecule runs are time-averaged for 1 to 2 x 10time steps. No significant differences in various DSMC results are observed. However, the higher-resolution cases converged faster. The predictions of various DSMC models agree well with the linearized Boltzmann solutions obtained by (Ohwada et al., 1989a).


Along with these possible error sources and limitations there are some disadvantages of the DSMC method applied to gas microflows. These are:


1. Slow Convergence: The error in the DSMC method is inversely proportional to the square root of the number of simulated molecules. Reducing the error by a factor of two requires increasing the number of simulated molecules by a factor of four! This is a very slow convergence rate compared to continuum-based simulations with spatial accuracy of second or higher order. Hence, if the continuum equations


(ЧГА).П    (ЧГА).П





Y    Y




Y    Y


FIGURE 15.2. Nondimensionalized velocity distribution across the channel for Kn = 0.1 and Kn = 2.0 flows. Comparisons of various DSMC resolutions against the linearized Boltzmann solution of (Ohwada et al., 1989a) are presented. It is seen that the DSMC simulations using the VSS (left) and VHS (right) models are in good agreement with the linearized Boltzmann solutions.

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