Analysis of discretization in the direct simulation Monte Carlo

Hadjiconstantinou, Nicolas G.

doi:10.1063/1.1289393

Cited by 172 publications

(96 citation statements)

References 7 publications

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“…It should also be noted that our numerical experiments have shown that the numerical error associated with VRDSMC is not strongly affected by other discretization parameters (e.g. Δy) and thus provided ε remains small, much like DSMC [1,13,15], accurate solutions can be obtained with fairly coarse grids and thus total numbers of particles that are not excessively large. Furthermore, this moderate increase in N cell is only practically limiting in applications characterized by Kn 1, while most transition regime flows can be described to engineering accuracy with N cell = O(100), which is not substantially higher than the number of particles per cell required by DSMC.…”

Section: Approximation Error and Limitationsmentioning

confidence: 99%

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Low-variance direct Monte Carlo simulations using importance weights

Al-Mohssen¹,

Hadjiconstantinou²

2010

ESAIM: M2AN

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Abstract. We present an efficient approach for reducing the statistical uncertainty associated with direct Monte Carlo simulations of the Boltzmann equation. As with previous variance-reduction approaches, the resulting relative statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the characteristic value of quantity of interest) is small and independent of the magnitude of the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible. In contrast to previous variance-reduction methods, the method presented here is able to substantially reduce variance with very little modification to the standard DSMC algorithm. This is achieved by introducing an auxiliary equilibrium simulation which, via an importance weight formulation, uses the same particle data as the non-equilibrium (DSMC) calculation; subtracting the equilibrium from the non-equilibrium hydrodynamic fields drastically reduces the statistical uncertainty of the latter because the two fields are correlated. The resulting formulation is simple to code and provides considerable computational savings for a wide range of problems of practical interest. It is validated by comparing our results with DSMC solutions for steady and unsteady, isothermal and non-isothermal problems; in all cases very good agreement between the two methods is found.Mathematics Subject Classification. 60H30, 76P05.

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Section: Approximation Error and Limitationsmentioning

confidence: 99%

“…A convergence proof for this algorithm can be found in [27]; an analysis of the error associated with the timestep discretization can be found in [13,15]. Here, we use a form of the collision integral that is convenient for discussing particle methods [4,5,19].…”

Section: Variance Reduction Using Importance Weights: Vrdsmcmentioning

confidence: 99%

Low-variance direct Monte Carlo simulations using importance weights

Al-Mohssen¹,

Hadjiconstantinou²

2010

ESAIM: M2AN

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“…The linear dimensions of the cells should be small in comparison with the length scale of the macroscopic §ow gradients normal to the streamwise directions, which means that the cell dimensions should be of the order or smaller than the local mean free path [27,28]. The time step should be chosen to be su©ciently small in comparison with the local mean collision time [29,30]. A very small time step results in an ine©cient advancement of the solution and accumulation of statistics.…”

Section: Free-stream and Flow Conditionsmentioning

confidence: 99%

Computational analysis of a rarefied hypersonic flow over combined gap/step geometries

Leite

Santos

2015

Progress in Flight Physics – Volume 7

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This work describes a computational analysis of a hypersonic §ow over a combined gap/step con¦guration at zero degree angle of attack, in chemical equilibrium and thermal nonequilibrium. E¨ects on the §ow-¦eld structure due to changes on the step frontal-face height have been investigated by employing the Direct Simulation Monte Carlo (DSMC) method. The work focuses the attention of designers of hypersonic con¦gurations on the fundamental parameter of surface discontinuity, which can have an important impact on even initial designs. The results highlight the sensitivity of the primary §ow¦eld properties, velocity, density, pressure, and temperature due to changes on the step frontal-face height. The analysis showed that the upstream disturbance in the gap/step con¦guration increased with increasing the frontal-face height. In addition, it was observed that the separation region for the gap/step con¦gura-tion increased with increasing the step frontal-face height. It was found that density and pressure for the gap/step con¦guration dramatically increased inside the gap as compared to those observed for the gap con¦guration, i. e., a gap without a step.

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“…It has been shown [10], [11] that the error in the transport coefficients is proportional to the square of the timestep, with a proportionality constant such that for timesteps of the order of one mean free time the error is of the order of 5%. In our simulations, ∆t < λ/(7c o ), thus making the error negligible.…”

Section: B Simulationsmentioning

confidence: 99%

Statistical error in particle simulations of low Mach number flows

Hadjiconstantinou¹,

Garcia²

2001

Computational Fluid and Solid Mechanics

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Abstract-We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flowfield scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified.

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Analysis of discretization in the direct simulation Monte Carlo

Cited by 172 publications

References 7 publications

Low-variance direct Monte Carlo simulations using importance weights

Low-variance direct Monte Carlo simulations using importance weights

Computational analysis of a rarefied hypersonic flow over combined gap/step geometries

Statistical error in particle simulations of low Mach number flows

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