Interdisciplinary Applied Mathematics

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causes statistical scatter only at the information level, which is smaller than the average macroscopic velocity of the system, typically on the order of 1 m/s. Therefore, the DSMC-IP method can be used for simulation of gas microflows. The information-preservation algorithm requires about 37.5% memory increase, compared to a regular DSMC algorithm. Since the DSMC-IP reduces the statistical scatter, it is possible to identify convergence to steady state by monitoring the average number density and streamwise velocity (or the kinetic energy) of the system. This approach cuts down the sample size and correspondingly decreases the CPU time required by a standard DSMC method for low-speed flows by orders of magnitude.


In Figure 15.3, we present a typical result from (Boyd and Sun, 2001). A comparison of density contours obtained from the DSMC, DSMC-IP, and Navier-Stokes with slip simulations for flow past an NACA 0012 airfoil is shown. The free stream flow conditions correspond to M = 0.1, Re = 1, Kn = 0.013. The computational domain consists of 9120 nonuniform structured cells, which are clustered near the airfoil. Each DSMC cell has 45 particles on average, while the DSMC-IP has 40 particles per cell. The time step is set to 5 x 10~8 s, which is smaller than the mean collision time of the particles. Both the DSMC and DSMC-IP are executed for 30,000 iterations to reach a steady state, before sampling the flow field. The sampling continued until each cell had an average of 400,000 sampled particles (corresponding to about 1000 samples per cell). Large statistical scatter is observed in the density contours obtained in the DSMC algorithm, as shown in Figure 15.3 (a). However, the density contours of the DSMC-IP are smooth, and agree well with the Navier-Stokes with slip results (plot in

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