Large statistical scatter and effective pressure boundary conditions are two critical problems in the computation of microchannel ows with the direct simulation Monte Carlo (DSMC) method. To address these issues, an extension of the DSMC-IP (information preservation) coupled method is developed from the one-dimensionalcase to the twodimensional case for microchannel ow. Simulation results in a microchannel ow from DSMC, IP, and numerical and analytical solutions to the Navier-Stokes equations are compared. The DSMC-IP coupled method successfully reduces the large statistical scatter usually obtained with DSMC in such low-speed ow systems. It also provides a suitable implementation of pressure boundary conditions. Introduction MICROCHANNELS are an important componentof many microelectrical mechanical systems (MEMS). 1 Successful numerical simulation of the ow eld inside these devices is required to understand small scale ow phenomena. Adopting a standard computational uid dynamics (CFD) technique is not appropriate because CFD is based on the continuum assumption, which is only good for the continuum regime (Kn < 0.001), and acceptable for the temperature jump and velocity slip region (0.001 < Kn < 0.1) if a slip wall condition is adopted instead of nonslip boundary conditions. However, for microchannel ows under experimental conditions, 1 ¡ 4 the ows are sometimes in the transition regime (0.1 < Kn < 10). Here, rare ed effects are signi cant, and CFD methods are not reliable. The direct simulation Monte Carlo method (DSMC) 5 is accurate for all ow regimes because it is based on kinetic theory and does not rely on the continuum assumption. Many researchers have already performed much work on simulation of microchannel ow with the DSMC method.6 ¡ 10 However, there are still many dif culties, and in some researchers ' belief 8 it is impossible to use DSMC to simulate microchannel ows under experimental conditions. Indeed, there are many experimental results, but no corresponding DSMC simulations are reported yet. To statistically simulate the ow under experimental conditions, we must overcome two particular dif culties: statistical scatter and proper implementation of pressure boundary conditions. In this study we will discuss these dif culties in detail. A new technique, the DSMC-IP (information presentation) coupled method, is presented to address these problems. Two cases are computed in the present study: a simpli ed test case and a case under experimental conditions. Dif culties Associated with DSMC Calculation Statistical ScatterUsually, the ow velocity in microchannels under typical experimental conditions is very low. For example, in the experiments of Pong et al.,2 the inlet velocity is about 20 cm/s. If we suppose the velocity obeys a Maxwellian distribution,then at room temperature for nitrogen, the standard deviation is r = p (2RT ) = 422 m/s. If we suppose the sampling processes are totally independent from step to step, then the statistical scatter in the nal DSMC result will be r 0 = r / p N , ...

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This study analyses compressible gas flows through microchannels or microtubes, and develops two complete sets of asymptotic solutions. It is a natural extension of the previous work by Arkilic et al. on compressible flows through microchannels. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for the Reynolds and Mach numbers at the outlets. Second, based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure and temperature distributions of compressible gas flow inside the microchannels and microtubes with a relaxation of the isothermal assumption, which was previously used in many studies. Numerical simulations of compressible flows through a microchannel and a microtube are performed by solving the compressible Navier-Stokes equations, with velocity slip and temperature jump wall boundary conditions. The numerical simulation results validate the analytical results from this study.

Spacecraft propulsion systems, such as Hall thrusters, are designed and tested in large vacuum chambers. The pumping capacity of modern facilities makes it possible to maintain pressures as low as 10 −3 -10 −4 Pa. One fundamental concern for the vacuum chamber is the facility effects on the chamber performance. In this study, several free molecular models are developed to analyze the rarefied background flow inside a vacuum chamber equipped with two-sided vacuum pumps. These models lead to various sets of analytical results including velocity distribution functions for the background flow and formulas to compute the vacuum pump sticking coefficient. These results can be used to evaluate the performance of vacuum chambers and to aid constructing proper background flows for particle simulations of these systems. The results indicate that the background flow conditions can have a significant nonzero mean velocity and cannot be considered to be described by a Maxwellian velocity distribution. The models are applied to analyze the rarefied background flow in a specific vacuum chamber. Calculations of the sticking coefficient for flow of xenon in the vacuum chamber yield values close to 0.40 for cryogenic pumps. Several modifications of the background flow treatment for particle simulations are proposed with the aid of these analytical results.

A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.