Interdisciplinary Applied Mathematics

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Particle weight: We have already discussed the effect of noise in DSMC; this is particularly troubling to the convergence of the multiscale approach. The noise in the DSMC estimates can be controlled by decreasing the particle weight or by increasing the number of DSMC time steps. To evaluate the dependence of convergence on the particle weight, wp, simulations are


d = 0.0 um


ov ^



d    = 0.2 um


ov



d = 0.4 um


ov



d = 0.6 um


ov


FIGURE 15.11. The absolute error in the pressure boundary condition transferred from the continuum subdomain to the DSMC subdomain for different overlaps. Nstep = 5000 is used.


performed using particle weights of 25 x 104, 5 x 104, 104, and 103. We observed (see (Aktas and Aluru, 2002), for convergence plots) that a smaller particle weight, which accounts for more particles, exhibits better convergence characteristics with less noise. We also observed that the convergence is not delayed significantly because of a larger noise (due to a larger particle weight). Thus, we can conclude that the method is fairly robust. The observation that the coupled method converges when a large particle weight is used is important for application of the particle cloning method (Chen and Boyd, 1996) to speed up the DSMC simulation. The particle weight that should be selected according to the DSMC accuracy requirements is 103. However, a lower weight requires extensive CPU times, and the simulation time can be reduced by using a particle cloning method that starts with 16 times the desired weight of 103 and using four cloning steps to get the desired accuracy.

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