Solution of the Wang-Chang-Uhlenbeck master equation

Cheremisin, F. G.

doi:10.1134/1.1536219

Cited by 29 publications

(9 citation statements)

References 2 publications

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“…The initial distribution function on both sides of the discontinuity is described by the velocities and spectral levels. It has the form 1 For moderate Mach numbers, the SW structure in Nitrogen can be computed with real value of the spectral energy gap 0…”

Section: Computed Results (A) Shock Wave Structure In Nitrogen At Higmentioning

confidence: 99%

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Agarwal¹,

Chen²,

Cheremisin³

2008

Lecture Notes in Computational Science and Engineering

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The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a monoatomic gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. The solution of GBE requires modeling of transition probabilities, elastic and inelastic cross-sections etc. of a diatomic gas molecule, needed for the solution of the collision integral. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

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Section: Computed Results (A) Shock Wave Structure In Nitrogen At Higmentioning

confidence: 99%

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Agarwal¹,

Chen²,

Cheremisin³

2008

Lecture Notes in Computational Science and Engineering

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“…It sharply increased the accuracy of calculations in near equilibrium area of the flow, in particular for low perturbed, low-speed flows. Further developments of the method consisted in improvements of some numerical techniques for speed up of the calculations and to extend the method on molecular gases with internal degrees of freedom (Tcheremissine, 2002(Tcheremissine, , 2005.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Boltzmann Kinetic Equation for Low Speed Flows

Tcheremissine

2008

Transport Theory and Statistical Physics

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“…For these simulations, the typical number of velocity nodes (in each direction) is 15-20 depending on the Mach number and mass ratio of gas species. The kinetic solver has been extended to molecular gases with internal degrees of freedom following the work [14]. Figure 3 shows the shock wave (SW) structure in Nitrogen at M=12.9 with the center of SW located at X=0.…”

Section: Molecular Gases and Gas Mixturesmentioning

confidence: 99%

Coupling Atomistic and Continuum Models for Multi-scale Simulations of Gas Flows

Kolobov

Arslanbekov

Vasenkov

2007

Computational Science – ICCS 2007

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Abstract. This paper describes two computational tools linking atomistic and continuum models of gaseous systems. The first one, a Unified Flow Solver (UFS), is based on a direct Boltzmann solver and kinetic CFD schemes. The UFS uses an adaptive mesh and algorithm refinement procedure for automatic decomposition of computational domain into kinetic and continuum parts. The UFS has been used for a variety of flow problems in a wide range of Knudsen and Mach numbers. The second tool is a Multi-Scale Computational Environment (MSCE) integrating CFD tools with Kinetic Monte Carlo (KMC) and Molecular Dynamics (MD). The MSCE was applied for analysis of catalytic growth of vertically aligned carbon nanotubes (CNT) in a C 2 H 2 /H 2 inductively coupled plasma. The MSCE is capable of predicting paths for delivering carbon onto catalyst/CNT interface, formation of single wall or multi-wall CNTs depending on the shape of catalyst, and transition from nucleation to the steady growth of CNTs.

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Solution of the Wang-Chang-Uhlenbeck master equation

Cited by 29 publications

References 2 publications

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Solution of the Boltzmann Kinetic Equation for Low Speed Flows

Coupling Atomistic and Continuum Models for Multi-scale Simulations of Gas Flows

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