Low-noise Monte Carlo simulation of the variable hard sphere gas

Radtke, Gregg Arthur; Hadjiconstantinou, Nicolas G.; Wagner, Wolfgang

doi:10.1063/1.3558887

Cited by 66 publications

(65 citation statements)

References 40 publications

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“…Extending the length would also reduce the signal-to-noise ratio, so there is a practical limit to DSMC being a viable tool to provide this kind of information. However, variance reduction techniques [30] offer the promise of extending particle techniques to very low speed flows.…”

Section: Discussionmentioning

confidence: 99%

A DSMC investigation of gas flows in micro-channels with bends

et al. 2013

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This version is available at https://strathprints.strath.ac.uk/42237/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.A DSMC investigation of gas flows in micro-channels with bends Monte Carlo (DSMC) solver, and benchmarked against simple micro-channel flow cases found in the literature. DSMC simulations are then carried out of gas flows for varying degrees of rarefaction along micro-channels with both one and two 90-degree bends. The results are compared to those from the equivalent straight micro-channel geometry. Away from the immediate bend regions, the pressure and Mach number profiles do not differ greatly from those in straight channels, indicating that there are no significant losses introduced when a bend is added to a micro-channel geometry. It is found that the inclusion of a bend in a micro-channel can increase the amount of mass that a channel can carry, and that adding a second bend produces a greater mass flux enhancement. This increase happens within a small range of Knudsen number (0.02 6 Kn in 6 0.08). Velocity slip and shear stress profiles at the channel walls are presented for the Knudsen showing the largest mass flux enhancement.

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Section: Discussionmentioning

confidence: 99%

A DSMC investigation of gas flows in micro-channels with bends

et al. 2013

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“…8,25 An exhaustive review of the ongoing discussion of thermal transport in graphene is beyond the scope of this paper whose primary objective is the presentation and validation of a new method for solving the Boltzmann-Peierls equation (BPE) with ab initio scattering for temporally and spatially dependent problems. The proposed method is based on the deviational simulation Monte Carlo framework used to simulate both rarefied gases [26][27][28] and phonon transport in the relaxation-time approximation. [29][30][31] In the present paper, it is extended to include phonon dispersion relations and, via the linearized ab initio three phonon scattering operator, [32][33][34] anharmonic force constants calculated from density functional perturbation theory (DFPT).…”

Section: Introductionmentioning

confidence: 99%

Deviational simulation of phonon transport in graphene ribbons with ab initio scattering

Landon

Hadjiconstantinou

2014

Journal of Applied Physics

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We present a deviational Monte Carlo method for solving the Boltzmann-Peierls equation with ab initio 3-phonon scattering, for temporally and spatially dependent thermal transport problems in arbitrary geometries. Phonon dispersion relations and transition rates for graphene are obtained from density functional theory calculations. The ab initio scattering operator is simulated by an energy-conserving stochastic algorithm embedded within a deviational, low-variance Monte Carlo formulation. The deviational formulation ensures that simulations are computationally feasible for arbitrarily small temperature differences, while the stochastic treatment of the scattering operator is both efficient and exhibits no timestep error. The proposed method, in which geometry and phonon-boundary scattering are explicitly treated, is extensively validated by comparison to analytical results, previous numerical solutions and experiments. It is subsequently used to generate solutions for heat transport in graphene ribbons of various geometries and evaluate the validity of some common approximations found in the literature. Our results show that modeling transport in long ribbons of finite width using the homogeneous Boltzmann equation and approximating phonon-boundary scattering using an additional homogeneous scattering rate introduces an error on the order of 10% at room temperature, with the maximum deviation reaching 30% in the middle of the transition regime.

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“…A simulation method using the above construct reduces to a method for simulating the dynamics of the deviation from equilibrium f d = f − f 0 ; such a method has been developed [32,[50][51][52] and is referred to as low-variance deviational simulation Monte Carlo (LVDSMC), which highlights its connection to DSMC to which it is related. LVDSMC proceeds in time using the standard splitting scheme (2.10) and (2.11) on the 'deviational population' of signed particles (i.e.…”

Section: Algebraic Decomposition and Variance Reductionmentioning

confidence: 99%

On efficient simulations of multiscale kinetic transport

Radtke

Péraud

Hadjiconstantinou

2013

Phil. Trans. R. Soc. A.

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We discuss a new class of approaches for simulating multiscale kinetic problems, with particular emphasis on applications related to small-scale transport. These approaches are based on a decomposition of the kinetic description into an equilibrium part, which is described deterministically (analytically or numerically), and the remainder, which is described using a particle simulation method. We show that it is possible to derive evolution equations for the two parts from the governing kinetic equation, leading to a decomposition that is dynamically and automatically adaptive, and a multiscale method that seamlessly bridges the two descriptions without introducing any approximation . Our discussion pays particular attention to stochastic particle simulation methods that are typically used to simulate kinetic phenomena; in this context, these decomposition approaches can be thought of as control-variate variance-reduction formulations, with the nearby equilibrium serving as the control. Such formulations can provide substantial computational benefits in a broad spectrum of applications because a number of transport processes and phenomena of practical interest correspond to perturbations from nearby equilibrium distributions. In many cases, the computational cost reduction is sufficiently large to enable otherwise intractable simulations.

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Low-noise Monte Carlo simulation of the variable hard sphere gas

Cited by 66 publications

References 40 publications

A DSMC investigation of gas flows in micro-channels with bends

A DSMC investigation of gas flows in micro-channels with bends

Deviational simulation of phonon transport in graphene ribbons with ab initio scattering

On efficient simulations of multiscale kinetic transport

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