Interdisciplinary Applied Mathematics

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where Q is the volumetric flowrate per unit width of the channel, h is the channel height, T0 is reference temperature, and R is the specific gas constant. The DSMC data is incorporated in the figure by plotting the mass flowrate data as a function of average Kn in the channel, since

M — Q P.

The error bars in the plot correspond to maximum fluctuations in the global mass balance and statistical scatter in pressure gradient (dP/dx), which is used here as an accuracy criterion. Knudsen’s minimum is clearly captured by the DSMC results at Kn « 1.0. The DSMC solution is compared with the semianalytic solutions of (Cercignani and Daneri, 1963), where the linearized Boltzmann equations are solved with the BGK model. Also, a comparison with numerical solutions of (Huang et al., 1997) is shown. These solutions were obtained from the linearized Boltzmann equations with the BGK model using the discrete ordinate method; see also (Siewert, 2000). The integrals involved were approximated by various orders (n) of Gauss quadrature. It is seen that Cercignani and Daneri’s results are recovered as (n) is increased. The current DSMC results match the Boltzmann solution quite well up to Kn = 2. Beyond this value, the DSMC results follow the seventh-order quadrature solution of (Huang et al., 1997), and subsequently become asymptotic to a constant value in the free-molecular flow regime, rather than increasing logarithmically. The reason for deviations of the DSMC data from the theoretical solution for infinitely long channels is the finite length of the channel (L/h = 20) used in these simulations.

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