This paper describes the development and application of a multiscale method for the efficient simulation of a large class of low-speed internal rarefied gas flows. The method is an extension of the hybrid atomistic-continuum approach recently proposed by Borg et al (2013) [J. Comp. Phys., 233, pp 400–413] for the simulation of micro/nano flows of high-aspect ratio. The extension is twofold: 1) a modification to accommodate fluid compressibility; and 2) implementation using a direct simulation Monte Carlo (DSMC) method for the treatment of dilute rarefied gas flows. The method is applied to a pair of internal-flow configurations: flow through a converging-diverging channel and eccentric cylindrical Couette flow. For validation/verification purposes, the multiscale simulation results are compared to those obtained from a full-scale DSMC simulation: very close agreement is obtained in all cases. The multiscale simulation is an order of magnitude more computationally efficient than the full-scale DSMC for the first test case, and two orders of magnitude more efficient for the second case.

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