Monte Carlo Simulation of Gas Flows

Bird, G. A.

doi:10.1146/annurev.fl.10.010178.000303

Cited by 214 publications

(108 citation statements)

References 19 publications

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“…The basis of the DSMC method, first formulated by Bird in the 1970's [2], is to circumvent the direct solution of the Boltzmann equation by considering a probabilistic simulation. It is categorized as a particle method, in which each simulation particle represents a large number of real gas atoms or molecules.…”

Section: Computers and Fluids 39 (2010) 2078-2089mentioning

confidence: 99%

“…The DSMC code presented in this paper has been formally titled dsmcFoam and is based on Bird's original formulation [2]. The open source nature of the new code, its unlimited parallel solution capability, and its potential application to 3D, arbitrary geometries are highlighted.…”

Section: Computers and Fluids 39 (2010) 2078-2089mentioning

confidence: 99%

“…The Direct Simulation Monte Carlo (DSMC) method [1,2] is the dominant numerical technique for solving engineering problems where the flow is rarefied. When applied properly, solutions to very complex flows involving chemical reactions, ionization and high degrees of molecular non-equilibrium are achievable.…”

Section: Introductionmentioning

confidence: 99%

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An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

Scanlon¹,

Roohi²,

White³

et al. 2010

Computers & Fluids

262

132

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Section: Computers and Fluids 39 (2010) 2078-2089mentioning

confidence: 99%

Section: Computers and Fluids 39 (2010) 2078-2089mentioning

confidence: 99%

See 1 more Smart Citation

An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

Scanlon¹,

Roohi²,

White³

et al. 2010

Computers & Fluids

262

132

View full text Add to dashboard Cite

“…DSMC was originally designed for aerospace applications in dilute gases, and thus has been thoroughly tested for high Kn flows (> 0.2). It has been applied to hypersonic and rarefied gas flows, and has in fact become the principle method for high Kn simulations [15][16][17][18]. DSMC has also been successfully applied to modeling chemical reactions [19][20][21], simluating blast-structure interactions at low Kn [22], and to study sound in dilute gases (high Kn) [23].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Acoustics in Diatomic Gases Using Direct Simulation Monte Carlo

Danforth

Long²

2005

AIP Conference Proceedings

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Abstract. The Direct Simulation Monte Carlo (DSMC) method has been very successful for the study of many problems in rarefied gas dynamics and hypersonic flow. The extension to applications such as acoustics will provide a useful tool for capturing all physical properties of interest for nonlinear acoustic problems, such as dispersion, attenuation, harmonic generation and nonequilibrium effects. The validity of DSMC for the entire range of Knudsen numbers (Kn), where Kn is defined as the mean free path divided by the wavelength, allows for the exploration of sound propagation at low Kn (low frequency, atmospheric conditions) as well as sound propagation at high Kn (high frequency, dilute gases, or in microdevices). This paper will present the application of DSMC to nonlinear acoustics in monatomic and diatomic gases for varying values of Kn.

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“…7, where we sketched a scenario for nonequilibrium systems in stationary states. Finally, the Boltzmann equation provides an elegant way to derive equilibrium distribution functions such as the famous Maxwell-Boltzmann distribution in momentum space.From a computational point of view, several modern simulation techniques, particularly in the field of fluid dynamics, are based on Boltzmann's stochastic stream-and-collide idea [103,104,105,106,107,108,109]. At first sight, however, Computer simulation in statistical mechanics 25 it is not immediately clear what the advantages of such a perspective are.…”

mentioning

confidence: 99%

Realizing Boltzmann's dream: computer simulations in modern statistical mechanics

Dellago

Posch

2008

ESI Lectures in Mathematics and Physics

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Abstract. Today, computer simulations belong to the most important and powerful theoretical tools for the investigation of statistical mechanical systems particularly in the field of condensed matter. Many simulation methods may directly, or indirectly, be traced back to ideas of Ludwig Boltzmann or are used to carry on the program he had envisioned. Using several illustrative examples, we discuss the role of computer simulation in modern statistical mechanics and, in particular, its relation to Boltzmann's legacy.1 What if? What would Boltzmann have done with a computer? Of course, any answer to this question is highly speculative, but it is easy to imagine that Boltzmann 2 C. Dellago and H. A. Posch would have realized what a wonderful tool for scientific research and discovery the computer is, particularly in his field of statistical mechanics. Most likely, Boltzmann would have invented the molecular dynamics method and used it to test and further develop the molecular models of matter he and his contemporaries created. All he required he already knew, and his motivation is more than clear from his work. With such simulations, Boltzmann literally could have watched how a system relaxes towards equilibrium, and he could have performed a numerical analysis of the validity of the assumption of molecular chaos, which is so central to his kinetic equation. Certainly, he would have determined the equations of state of dilute gases and of dense liquids and solids. One may further speculate that Boltzmann would have made creative use of modern visualization tools that, today, are of such crucial importance in simulation studies and provide insight and guidance not availiable otherwise. It is also amusing to think about what Boltzmann would not have done, if he had had access to a computer. For instance, would Boltzmann have bothered to write down the Boltzmann equation? Perhaps he would just have run a molecular dynamics simulation for hard spheres with simple collision rules to follow the dynamics of his model gas. From such a simulation he could have calculated properties of dilute and dense gases in order to compare them with experimental data. Then, the need to write down an approximate and complicated integro-differential equation that cannot even be solved analytically except for very simple cases would not have arisen. Or would Boltzmann have tried to develop a virial expansion for the hard sphere gas if he could have determined the equation of state with high precision from simulations? Nobody knows, but statistical mechanics might have unfolded in a completely different way, if computers had been available at Boltzmann's time. While it is not hard to imagine where Boltzmann would have begun his computational investigation, it is impossible to predict where insights gleaned from simulations would have taken a mind like his.In this article we will take a more modest attitude and reflect on the significance of computer simulations in the research program initiated by Boltzmann and his contemporaries. Since t...

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Monte Carlo Simulation of Gas Flows

Cited by 214 publications

References 19 publications

An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries

Nonlinear Acoustics in Diatomic Gases Using Direct Simulation Monte Carlo

Realizing Boltzmann's dream: computer simulations in modern statistical mechanics

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