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Journal ArticleDOI

Conservative Species Weighting Scheme for the Direct Simulation Monte Carlo Method

Iain D. Boyd1
01 Oct 1996-Journal of Thermophysics and Heat Transfer (American Institute of Aeronautics and Astronautics Inc. (AIAA))-Vol. 10, Iss: 4, pp 579-585
TL;DR: In this paper, a new numerical scheme for the simulation of trace species is proposed, which explicitly conserves both linear momentum and energy during collisions, and is applied to a number of problems.
Abstract: The direct simulation Monte Carlo method (DSMC) finds application to nonequilibriu m gas flows including hypersonic aerodynamics, spacecraft propulsion, materials synthesis, and flows in microma- chines. In many of these problems, the species of most interest are present in very small quantities. This presents a resolution problem for the DSMC technique in which a finite number of particles is employed. This study proposes a new numerical scheme for the simulation of trace species. Unlike an existing scheme, the new method explicitly conserves both linear momentum and energy during collisions. The scheme is applied to a number of problems to demonstrate its accuracy and utility. Reduced execution times and improved resolution of trace species properties may be obtained simultaneously with the new method. HE direct simulation Monte Carlo method (DSMC) is a physically accurate method for the computation of non- equilibrium gas flows. The technique is most useful in circum- stances where there are insufficient numbers of collisions in the flow to maintain the equilibrium forms of the distribution functions describing the various energy modes of the gas. Gen- erally, such conditions prevail when the average distance be- tween successive collisions of each particle, the mean free path, is comparable to the characteristic length scale of the flow. This type of nonequilibrium condition occurs in a variety of problems of current interest. These include hypersonic flows around vehicles flying at high altitude in planetary atmo- spheres, flows from small rockets used on satellites for control, flows involved in the synthesis of thin films, and flows in mi- cron-scale mechanical structures. The DSMC method employs particles simulated in the com- puter to represent the motions and collisions of real molecules and atoms. A typical simulation employs a few million parti- cles to represent the much larger number of real molecules. The particle weight W is the number of real molecules that each simulated particle represents. The basic assumption of the technique is that particle motion may be performed separately from particle collisions over a time step that is small compared to the average time between successive collisions of the same particle. In the DSMC method, particle motions and collisions are performed in the physical domain. Particles are moved through the length specified by the product of the time step and the velocity vector of each particle. The particles are then collected into cells, and only those particles that occupy a par- ticular cell are considered possible collision candidates. Col- lision selection is performed using statistical probability mod- els that are derived from basic kinetic theory. Macroscopic flow properties are obtained by time averaging particle prop- erties in the computational cells over several thousand itera- tions of the basic algorithm. In many of the applications of interest, the chemical species of most importance occur in very small quantities. To illustrate this point, one particular example is considered. The Bow Shock Ultra Violet (BSUV) flight experiments1'2 were designed
Citations
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Journal ArticleDOI
TL;DR: In this article, the principles of and procedures for implementing direct simulation Monte Carlo (DSMC) are described and guidelines to inherent and external errors common in DSMC applications are provided.
Abstract: ▪ Abstract The principles of and procedures for implementing direct simulation Monte Carlo (DSMC) are described. Guidelines to inherent and external errors common in DSMC applications are provided. Three applications of DSMC to transitional and nonequilibrium flows are considered: rarefied atmospheric flows, growth of thin films, and microsystems. Selected new, potentially important advances in DSMC capabilities are described: Lagrangian DSMC, optimization on parallel computers, and hybrid algorithms for computations in mixed flow regimes. Finally, the limitations of current computer technology for using DSMC to compute low-speed, high–Knudsen-number flows are outlined as future challenges.

386 citations

Journal ArticleDOI
TL;DR: In this paper, the particle-in-cell and direct simulation Monte Carlo (DSMC) approaches have been combined into a PIC-DSMC model for self-consistent simulations of low-temperature collisional plasmas and the background gas.
Abstract: The particle-in-cell (PIC) and direct simulation Monte Carlo (DSMC) approaches have been combined into a PIC-DSMC model for self-consistent simulations of low-temperature collisional plasmas and the background gas. This novel approach is based on the weighting collision simulation scheme allowing for disparate number densities and time scales of different species. The applicability of the developed algorithm is illustrated by simulations of one-dimensional direct current and two-dimensional magnetron sputtering discharges in argon. An appreciable effect of the energetic discharge species on the density, temperature, and flow field of the background gas shows the importance of the coupled plasma-gas simulation for such technologies as sputtering, dry etching, plasma enhanced vapor deposition, etc.

98 citations


Cites background from "Conservative Species Weighting Sche..."

  • ...An alternative scheme, wherein these characteristics are modified by small values in the aftermath of each collision, has been recently proposed [ 36 ]....

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Journal ArticleDOI
TL;DR: In this article, the authors used direct simulation Monte Carlo (DSMC) to model the ionizing reaction probability of a hypersonic vehicle entering the Earth's atmosphere from space.
Abstract: When vehicles reenter the Earth’s atmosphere from space, the hypersonic conditions are sufficiently energetic to generate ionizing reactions. The production of a thin plasma layer around a hypersonic vehicle can block radio waves sent to and from the vehicle, leading to communications blackout. For Earth entry from orbit, the maximum energy involved in molecular collisions requires only associative ionization of air-species to be considered. In the present study, the modeling of such reactions is considered in detail using the direct simulation Monte Carlo (DSMC) method. For typical Earth entry conditions, with a velocity near 8km∕s, it is shown that the average ionizing reaction probabilities are small. Special numerical techniques must therefore be used in the DSMC technique in order to numerically resolve these reactions. Additional simulation problems arise from the relatively small mass of the electrons in comparison to the other atoms and molecules in these flow fields. Artificially increasing the e...

67 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a differentially weighted time-driven Monte Carlo (DSMC) method, which captures the coagulation dynamics in dispersed systems with low noise and is simultaneously able to track the size distribution over the full size range.
Abstract: The direct simulation Monte Carlo (DSMC) method is widely utilized to simulate microscopic dynamic processes in dispersed systems that give rise to the population balance equation In conventional DSMC approaches, simulation particles are equally weighted, even for broad size distributions where number concentrations in different size intervals are significantly different The resulting statistical noise and limited size spectrum severely restrict the application of these DSMC methods This study proposes a new Monte Carlo (MC) method, the differentially weighted time-driven method, which captures the coagulation dynamics in dispersed systems with low noise and is simultaneously able to track the size distribution over the full size range Key elements of this method include constructing a new jump Markov process based on a new coagulation rule for two differentially weighted simulation particles, and restricting the number of simulation particles in each size interval within prescribed bounds The method

60 citations


Additional excerpts

  • ...Although the concept of differentially weighted simulation particles is widely applied in the classical DSMC for the computation of nonequilibrium gas flows (Boyd 1996) and Coulomb collisions in plasmas (Nanbu and Yonemura 1998), it is seldom adopted by PBE-MC for particle dynamics....

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References
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Book
16 Jun 1994
TL;DR: The direct simulation Monte Carlo (or DSMC) method has, in recent years, become widely used in engineering and scientific studies of gas flows that involve low densities or very small physical dimensions as mentioned in this paper.
Abstract: The direct simulation Monte Carlo (or DSMC) method has, in recent years, become widely used in engineering and scientific studies of gas flows that involve low densities or very small physical dimensions. This method is a direct physical simulation of the motion of representative molecules, rather than a numerical solution of the equations that provide a mathematical model of the flow. These computations are no longer expensive and the period since the 1976 publication of the original Molecular Gas Dynamics has seen enormous improvements in the molecular models, the procedures, and the implementation strategies for the DSMC method. The molecular theory of gas flows is developed from first principles and is extended to cover the new models and procedures. Note: The disk that originally came with this book is no longer available. However, the same information is available from the author's website (http://gab.com.au/)

5,311 citations

Book
01 Jan 1976

1,359 citations

Journal ArticleDOI
TL;DR: In this article, a numerical method to compute a two-dimensional hypersonic flowfield that is weakly ionized and in thermochemical nonequilibrium has been developed, described by coupled partial differential equations for the conservation of species mass, mass-averaged momentum, vibrational energy of each diatomic species, electron energy, and total energy.
Abstract: A numerical method to compute a two-dimensional hypersonic flowfield that is weakly ionized and in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partial differential equations for the conservation of species mass, mass-averaged momentum, vibrational energy of each diatomic species, electron energy, and total energy. The steady-state solution to these fully coupled equations has been obtained for a gas composed of seven chemical species and characterized by six temperatures using an implicit Gauss-Seidel line relaxation technique. The computed electron number densities in the flowfield of a sphere cone compare well with experimental results.

450 citations

Journal Article
TL;DR: In this article, the relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation.
Abstract: The relationships between various numerical methods applied to problems in rarefied gasdynamics are discussed, with emphasis on conflicting viewpoints and computational requirements associated with physical simulation versus the numerical solution of the Boltzmann equation. The basic differences between the molecular dynamics and direct simulation methods are shown to affect their applicability to dense and rarefied flows. Methods for the probabilistic selection of representative collision in the direct simulation Monte Carlo method are reviewed. A method combining the most desirable features of the earlier methods is presented.

135 citations

Journal ArticleDOI
TL;DR: The numerical performance of a Monte Carlo scheme used in the analysis of non-equilibrium gas dynamics has been greatly improved by careful implementation of the algorithm in order to take advantage of the vector hardware of supercomputers.

66 citations