A Method for Estimating the Computational Requirements of DSMC Simulations

The direct simulation Monte Carlo ͑DSMC͒ method is the preferred approach for simulating rarefied gas flows in complex geometries. However, the standard DSMC method becomes inefficient in the limit M = Ū / ͗c͘ → 0 when the thermal velocity fluctuations which scale with the speed of sound ͗c͘ are much larger than characteristic ensemble-averaged flow speed Ū . In this paper, we propose a modified DSMC algorithm which simulates the linearized Bhatnagar-Gross-Krook ͑BGK͒ approximation to the Boltzmann equation. The particles in this method are uniformly distributed in space and have a rest-state, equilibrium Maxwellian velocity distribution. The deviations from the equilibrium state are captured by weightings, indicating that each particle represents a noninteger expectation for finding gas molecules with the simulation particle's velocity in the spatial cell where it is found. The BGK approximation makes the implementation of such a method simple and efficient because the BGK collision rule can be implemented by adjusting particle weightings without the need to create new particles during the simulation. The method can be incorporated into existing DSMC simulation programs with minimal changes. We apply the new algorithm to two test problems-pressure-driven flow through a nanochannel and flow around an isolated sphere. Results obtained with the new method are in excellent agreement with previous theories and simulations.

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“…A detailed discussion on choosing various simulation parameters in the DSMC method is available in Ref. 17.…”

Section: Simulation Methodsmentioning

confidence: 99%

An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar–Gross–Krook model

Ramanathan

Koch

2009

Physics of Fluids

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“…Time is advanced in discrete steps such that each step is small in comparison with the mean collision time, which is defined as the mean time between the successive collisions suffered by any particular molecule. More details for estimating the computational requirements of DSMC simulations are presented at length by Rieffel (1999). The computational domain is made large enough so that the upstream and side boundaries can be specified as freestream conditions.…”

Section: Computational Methods and Proceduresmentioning

confidence: 99%

Leading-edge bluntness effects on aerodynamic heating and drag of power law body in low-density hypersonic flow

Santos¹

2005

J. Braz. Soc. Mech. Sci. & Eng.

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A numerical study is reported on power law shaped leading edges situated in a rarefied hypersonic flow. The sensitivity of the heat flux and drag coefficient to shape variations of such leading edges is calculated by using a Direct Simulation Monte Carlo method. Calculations show that the stagnation point heating on power law leading edges with finite radius of curvature follows the same relation for classical blunt body in continuum flow; it scales inversely with the square root of the curvature radius at the nose. Furthermore, for those leading edges with zero or infinity radii of curvature, the heat transfer behavior is in surprising agreement with that for classical blunt body far from the nose of the leading edge

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“…The choice of these parameters is similar to that for the standard DSMC method discussed in Ref. 27.…”

Section: -3mentioning

confidence: 97%

Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory

2010

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Nanoelectromechanical oscillators are very attractive as sensing devices because of their low power requirements and high resolution, especially at low pressures. While many experimental studies of such systems are available in the literature, a fundamental theoretical understanding over the entire range of operating conditions is lacking. In this article, we use our newly developed BhatnagarGross-Krook based low Mach number direct simulation Monte Carlo method to study the noncontinuum drag force acting on a cylinder oscillating normal to a wall. We explore quasisteady flows in which f Ӷ 1 as well as unsteady flows for which f = O͑1͒. Here is the oscillation frequency and f is the characteristic time for the development of the gas flow. The drag force per unit length acting on a long cylindrical wire is studied as a function of the Knudsen number, defined in terms of the mean free path and the radius of the cylinder R as Kn= / R. For quasisteady flows, we also present theoretical calculations for the slip regime, KnӶ 1, and the free molecular flow regime, Knӷ 1. Simulations of unsteady gas flow around a sinusoidally oscillating cylinder near a wall indicate that the drag force per unit length nondimensionalized by 4U approaches constant values for f Ӷ 1 ͑quasisteady flow͒ and for f ӷ 1. Here is the gas viscosity and U is the maximum value of the nanowire velocity. The simulation results are compared with experimental measurements in the quasisteady regime.

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A Method for Estimating the Computational Requirements of DSMC Simulations

Cited by 23 publications

References 17 publications

An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar–Gross–Krook model

An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar–Gross–Krook model

Leading-edge bluntness effects on aerodynamic heating and drag of power law body in low-density hypersonic flow

Noncontinuum drag force on a nanowire vibrating normal to a wall: Simulations and theory

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