Interdisciplinary Applied Mathematics

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are valid (for Kn < 0.1), it is computationally more efficient to use the continuum models than the DSMC method.

2. Large Statistical Noise: Microflows are typically low-speed flows (1 mm/s to 1 m/s). The macroscopic fluid velocities are obtained by averaging the molecular velocities (of approximate value 500 m/s) for a long time. This five to two orders of magnitude difference between the molecular and average speeds results in large statistical noise, thus microflows require a very long time averaging for gas microflow simulations. The statistical fluctuations decrease with the square root of the sample size. Time or ensemble averages of low-speed microflows on the order of 0.1 m/s require about 108 samples in order for one to be able to distinguish such small macroscopic velocities. A modified version was introduced by (Fan and Shen, 1999), who developed an information-preservation (IP) technique that enables DSMC simulation of low-speed flows at higher efficiency; see Section 15.1.3.

3. Long Time to Reach Steady State: For low-speed microflows the time required to reach steady state is usually dictated more by the convective time scales than the diffusive time scales. For example, gas flow in a microchannel of length 1 cm and height 1 yrm with an average speed of 1 cm/s will require the DSMC simulation to reach time 1 second for the macroscopic disturbances to travel from the inflow toward the outflow of the channel. On the other hand, the viscous time scale for this problem can be calculated by tv;sc « V/W v, where v is the kinematic viscosity (z/a;r « 10 6 m2/s), and h is the height of the channel. For air in a 1-p,m channel the viscous time scale is 10~3 seconds, a value three orders of magnitude less than    the    convective    time scale.    The    mean    collision    time    for    air    at

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