Convergence behavior of a new DSMC algorithm

The convergence rate of a new direct simulation Monte Carlo (DSMC) method, termed “sophisticated DSMC”, is investigated for one-dimensional Fourier flow. An argon-like hard-sphere gas at 273.15 K and 266.644 Pa is confined between two parallel, fully accommodating walls 1 mm apart that have unequal temperatures. The simulations are performed using a one-dimensional implementation of the sophisticated DSMC algorithm. In harmony with previous work, the primary convergence metric studied is the ratio of the DSMC-calculated thermal conductivity to its corresponding infinite-approximation Chapman–Enskog theoretical value. As discretization errors are reduced, the sophisticated DSMC algorithm is shown to approach the theoretical values to high precision. The convergence behavior of sophisticated DSMC is compared to that of original DSMC. The convergence of the new algorithm in a three-dimensional implementation is also characterized. Implementations using transient adaptive sub-cells and virtual sub-cells are compared. The new algorithm is shown to significantly reduce the computational resources required for a DSMC simulation to achieve a particular level of accuracy, thus improving the efficiency of the method by a factor of 2.     

Convergence of a Distributional Monte Carlo Method for the Boltzmann Equation

Direct Simulation Monte Carlo (DSMC) methods for the Boltzmann equation employ a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This representation limits the method to converge only weakly to the solution of the Boltzmann equation. Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and $L^\infty$ solutions of the Boltzmann equation. This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC. We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods. Toward this end, we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.     

具有局部稀薄气体效应的高超声速尖锥气动加热特征研究

以微钝尖锥为飞行器前缘模型,采用基于分子运动论的DSMC方法模拟不同前缘曲率半径的尖锥在高超声速来流下的气动热环境,计算驻点热流率,并与Fay-Riddell公式和其他修正理论作对比,研究具有局部稀薄气体效应的高超声速尖锥气动加热特征及其变化规律.发现修正的Cheng参数适合作为工程上判断驻点区域稀薄气体效应影响大小的判据.     

Formation of argon cluster with proton seeding

ABSTRACT

We employ force-field molecular dynamics simulations to investigate the kinetics of nucleation to new liquid or solid phases in a dense gas of particles, seeded with ions. We use precise atomic pair interactions, with physically correct long-range behaviour, between argon atoms and protons. Time dependence of molecular cluster formation is analysed at different proton concentration, temperature and argon gas density. The modified phase transitions with proton seeding of the argon gas are identified and analysed. The seeding of the gas enhances the formation of nano-size atomic clusters and their aggregation. The strong attraction between protons and bath gas atoms stabilises large nano-clusters and the critical temperature for evaporation. An analytical model is proposed to describe the stability of argon-proton droplets and is compared with the molecular dynamics simulations.     

Harmonically trapped jellium

We discuss the model of a D-dimensional confined electron gas in which the particles are trapped by a harmonic potential. In particular, we study the non-interacting kinetic and exchange energies of finite-size inhomogeneous systems, and compare the resulting Thomas–Fermi and Dirac coefficients with various uniform electron gas paradigms. We show that, in the thermodynamic limit, the properties of this model are identical to those of the D-dimensional Fermi gas.     

Solution of the one-dimensional linear Boltzmann equation for charged Maxwellian particles in an external field

The one-dimensional linear homogeneous Boltzmann equation is solved for a binary mixture of quasi-Maxwellian particles in the presence of a time-dependent external field. It is assumed that the charged particles move in a bath of neutral scatterers. The neutral scatterers are in thermal equilibrium and the concentration of the charged particles is low enough to neglect collisions between them. Two cases are considered in detail, the constant and the periodic external field. The quantities calculated are the equilibrium and the stationary distribution function, respectively, from which any desired property can be derived. The solution of the Boltzmann equation for Maxwellian particles can be reduced to the solution of the so-called cold gas equation by employing the one-dimensional variant of a convolution theorem due to Wannier. The two limiting cases, the Lorentz gas (m _A0) and the Rayleigh gas (m _A) are treated explicitly. Furthermore, by computing the central moments, the deviations from the Gaussian approximation are discussed, and in particular the large-velocity tails are evaluated.     

Recent Progress in Chemiluminescence for Gas Analysis

Abstract

Chemiluminescence is frequently used as a powerful analytical tool for gas analysis. In this mini-review with 102 references, we summarize the recent advances in chemiluminescence-based analytical methodologies and their application in gas/volatile species analysis, mainly including applications of ozone-induced chemiluminescence, cataluminescence-based gas sensors and arrays, and dielectric barrier discharge–induced chemiluminescence for gas analysis. Efforts in the innovation of the methodologies, the exploration of new sensing materials, and the mechanism studies are discussed in detail.     

Knudsen Layer for Gas Mixtures

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math. 39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.     

稀薄气体二维外部柱体绕流特性研究

本文采用直接模拟蒙特卡罗方法对稀薄气体二维外部柱体绕流问题进行了数值模拟。结果表明:外部绕流问题,在特定情况下会产生激波,激波的产生,不仅与气体的稀薄程度有关,还与来流马赫数有关。而气流与壁面之间的换热,随来流马赫数增加而增加,随气体稀薄程度增加而减小。     

Flow overshooting in crossing flow of lattice gas

We study the lattice gas flow of two components of biased-random walkers at a crossing under a periodic boundary. The lattice gas mixture consists of two components of particles (walkers) in which one component of particles moves north and the other component of particles moves east. The current (flow) increases with ρ_x (density of the east-bound particles) at low density and displays overshooting at an intermediate density. The flow overshooting occurs only for a certain range of ρ_y (density of the north-bound particles). Then clogging occurs and the current saturates. Furthermore, when the density is high, the current decreases with increasing density. The overshooting shown in the current-density (fundamental) diagram is due to the formation of an unstable oscillating jam just before clogging occurs. It is shown that flow overshooting does not occur in unidirectional flow through a porous medium but occurs in unidirectional flow through a group of Brownian particles.     

A hybrid particle approach for continuum and rarefied flow simulation

A hybrid particle scheme is presented for the simulation of compressible gas flows involving both continuum regions and rarefied regions with strong translational nonequilibrium. The direct simulation Monte Carlo (DSMC) method is applied in rarefied regions, while remaining portions of the flowfield are simulated using a DSMC-based low diffusion particle method for inviscid flow simulation. The hybrid scheme is suitable for either steady state or unsteady flow problems, and can simulate gas mixtures comprising an arbitrary number of species. Numerical procedures are described for strongly coupled two-way information transfer between continuum and rarefied regions, and additional procedures are outlined for the determination of continuum breakdown. The hybrid scheme is evaluated through a comparison with DSMC simulation results for a Mach 6 flow of N₂ over a cylinder, and good overall agreement is observed. Large potential efficiency gains (over three orders of magnitude) are estimated for the hybrid algorithm relative to DSMC in a simple example involving a rarefied expansion flow through a small nozzle into a vacuum chamber.     

On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard

A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann–Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings.     

The numerical simulation of two-dimensional aluminized composite solid propellent combustion

A numerical framework is presented which examines, for the first time, the burning of two-dimensional aluminized solid propellants. Aluminized composite propellants present a difficult mathematical and numerical challenge because of complex physics and topological changes that occur at the propellant surface. For example, both mathematical models and appropriate numerical solvers must describe the regressing burning surface, aluminium particle detachment and evolution throughout the gas-phase flow field, surface tension effects, ignition and combustion of aluminium particles, phase change effects, agglomeration of aluminium particles, radiation feedback to the propellant surface, to name a few. All of these effects must be modelled in a consistent manner. A numerical framework for which these effects can be included in a rational fashion is currently being developed. This framework includes the level set method to capture the solid–gas interface as well as particle motion in the gas phase. Some preliminary calculations of the two-dimensional combustion field supported by a disc pack with embedded aluminium particles are presented.     

Degenerate slightly nonideal Bose gas in a parabolic trap

The correction to the energy and the number of particles in excited oscillator states is found in the approximation of a pair interaction between the particles at close to zero temperature. It is shown that in the case of the traps used in experiments the gas starts to differ appreciably from an ideal gas when more than N=1000 particles are trapped. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 228–231 (25 August 1997)     

Gas pressure cell for electroluminescence and photoconductivity measurements

Abstract

High-pressure studies of electroluminescence and photoconductivity are commonly carried out using liquid pressure systems. The wider application of a gas pressure system (with its substantial advantages) in this kind of studies is limited by the difficulties in the construction of a suitable sample cell. Such a cell, in addition to electric and optical access, must be provided with a high-pressure inlet, and the overall dimension of the cell should allow it to fit most standard cryostats. In this paper a high gas pressure optical cell is described which enables electroluminescence or photoconductivity measurements at pressures up to 1.0 GPa and at temperatures down to 1K.     

How do quantum numbers generally vary in the adiabatic transformation of an ideal gas？

We continue to analyse the known law of adiabatic transformation for an ideal gas PV^5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.     

The runaway effect in a Lorentz gas

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦ ⁿ . Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < –1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.     

Coarse-grain modelling using an equation-of-state many-body potential: application to fluid mixtures at high temperature and high pressure

ABSTRACT

A many-body, coarse-grain model, termed the product gas mixture model, is presented that accurately describes the thermodynamic behaviour of molecular mixtures. The coarse-grain model is developed by first approximating the mixture as a van der Waals one-fluid, and subsequently applying an exponential-6 equation-of-state to describe the forces and energies between particles in the spirit of the many-body model pioneered by Pagonabarraga and Frenkel. Isothermal dissipative particle dynamics simulations are carried out at thermochemical states that occur during decomposition of a prototypical energetic material, RDX (1,3,5-trinitro-1,3,5-triazinane). The product gas mixture model performance is assessed by comparing to an explicit-molecule model and a hard-core coarse-grain model based on the exponential-6 pair potential. Overall, the many-body, coarse-grain model is shown to accurately capture the structural and thermodynamic properties for the wide variety of thermochemical states considered, while the hard-core coarse-grain model cannot. The many-body, coarse-grain model overcomes the issues of transferability, scaling consistency and unphysical ordered phase behaviour that often afflict coarse-grain models. While specific thermochemical conditions related to RDX decomposition are considered, the results are generally applicable to the thermodynamic behaviour of other fluid mixtures at both moderate and extreme conditions.     

Raman Spectroscopic Studies of Methane Gas Hydrates

Abstract

A brief review of the Raman spectroscopic studies of methane gas hydrates is given, supported by some new measurements done in our laboratory.