Interdisciplinary Applied Mathematics

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Finally, we must indicate that DSMC computations of more complex cases, such as the squeeze film damping (see Section 6.1), often require consideration of two- or three-dimensional unsteady flows. Although such computations are very challenging, ensemble averaging requires independent realizations of unsteady flows. This may enable code parallelization with perfect parallel efficiency if the stochastic processes as well as the random number generators employed in each processor are independent of each other.

15.1.3 DSMC: Information-Preservation Method

(Fan and Shen, 1999) have developed an information-preservation (IP) scheme for low-speed rarefied gas flows. Their method uses the molecular velocities of the DSMC method as well as an information velocity that records the collective velocity of a large number of molecules that a simulated particle represents. The information velocity is based on an inelastic collision model. The results presented for one-dimensional Couette, Poiseuille, and Rayleigh flows in the slip, transition, and free-molecular flow regimes show very good agreement with the corresponding analytical solutions. Also, Boyd and his co-workers have developed a DSMC-IP scheme for simulation of two-dimensional gas microflows (Cai et al., 2000). In (Sun and Boyd, 2002), a general two-dimensional unsteady IP formulation is described that relaxes the incompressible, isothermal assumptions of (Fan and Shen, 1999). The new IP version was shown in (Sun and Boyd, 2002), to provide good agreement with DSMC fundamental test cases including Couette flow and Rayleigh flow. This method was also used in (Sun and Boyd, 2004), to investigate fundamental aerodynamic behavior under flow conditions typical of microsystems.

The DSMC-IP method overcomes the statistical scatter in low-speed constant-density flow systems. The statistical scatter of DSMC is due to the thermal motion of particles with mean thermal speed, which is on the order of    450    m/s.    However    in    the    DSMC-IP    scheme,    the    thermal    motion

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