Solution to the Boltzmann kinetic equation for high-speed flows

Tcheremissine, F. G.

doi:10.1134/s0965542506020138

Cited by 96 publications

(62 citation statements)

References 4 publications

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“…(12) but φ(r) ≡ 0, were based on semi-regular numerical methods (Frezzotti and Sgarra, 1993). In these class of methods, developed for rarefied gas dynamics studies (Tcheremissine, 2006), the distribution function is discretized and the spatial advection term at the l.h.s. of Eq.…”

Section: Numerical Aspects Of Enskog-type Kinetic Equationsmentioning

confidence: 99%

Kinetic theory aspects of non-equilibrium liquid-vapor flows

Frezzotti

Barbante

2017

Mechanical Engineering Reviews

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Kinetic theory of fluids plays an important role in understanding and modeling mass, momentum and energy transfer between the vapor and liquid phase in non-equilibrium two-phase flows, in which evaporation and/or condensation take place. The paper presents a review of the literature which focuses on kinetic modeling of the vapor-liquid interface. Starting from the studies of the Knudsen layer structure in evaporation and condensation, the problem of the formulation of kinetic boundary conditions is described and discussed. The formulation of models based on approximate kinetic descriptions of dense fluids is described and the model capabilities are assessed through the analysis of the results obtained by various authors.

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Section: Numerical Aspects Of Enskog-type Kinetic Equationsmentioning

confidence: 99%

Kinetic theory aspects of non-equilibrium liquid-vapor flows

Frezzotti

Barbante

2017

Mechanical Engineering Reviews

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“…The collision integral is calculated by a projection method [4] which ensures strict conservation of mass, momentum, and energy, regardless of the number of points in the cubature grid, and makes the (collision) integral for a maxwellian distribution function, ƒ M , go to zero. This last property is especially important for computation of slow and weakly nonequilibrium flows, for which a locally maxwellian function is the main part of the solution.…”

mentioning

confidence: 99%

“…The Boltzmann equation is solved on a fixed spacevelocity grid by a finite-difference method and the collision integral is calculated by a regular method using multidimensional cubature grids [3,4]. We consider a monatomic gas with an arbitrary spherically symmetric interaction potential.…”

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confidence: 99%

Programming and modelling environment for studies of gas flows in micro- and nanostructures based on solving the Boltzmann equation

et al. 2008

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A set of programs has been developed for modelling gas flows in micro-and nanostructures. The programs are based on a method for solving the kinetic equation by a finite-difference technique on a fixed space-velocity grid. A projection method is used for calculating the Boltzmann collision integral which ensures that the conservation of mass, momentum, and energy is rigorously satisfied and that the collision integral goes to zero under thermodynamic equilibrium conditions. An explicit flux conservative scheme is used for approximating the differential part. The solution of the resulting system of difference equations is found by splitting into stages of collisional relaxation and free molecular flow. The computational algorithm is realized on a multiprocessor system using MPI technology. A graphical shell has been developed for visualizing the results during the computations and for convenient variation of the physical parameters of the flow under study. Some calculations of flows through a periodic system of square holes and a periodic system of slots whose transverse dimension is on the order of the mean free path of the gas molecules, as well as some model calculations of a micropump design, are given as examples.The development of micro-and nanotechnologies, the construction of microscopic vacuum pumps, filters, gas analyzers, manipulators, and other instruments, and research on techniques for the safe storage of hydrogen, as well as of toxic and radioactive gases, in nanostructures have stimulated interest in studies of gas flows in devices whose characteristic sizes are comparable to the molecular mean free path. The practical importance of these studies is explained by the need to evaluate the working characteristics of the planned devices over a wide range of physical parameters, which determine the properties of the gaseous medium and materials from which they are made. The equations of continuum hydrodynamics cannot be used for numerical modelling of these flows, so that it is necessary to use methods from the theory of rarefied gas flows [1].Computational techniques for the theory of rarefied gases were developed rapidly during the second half of the last century for aerospace applications. Two main approaches were developed: direct statistical modelling and finite-difference solution of the Boltzmann kinetic equation. In order to reduce the volume of calculations, model kinetic equations that were not rigorously justified but were simpler to solve were often used instead of the Boltzmann equation. In the first approach [2], the evolution of a large number of three dimensional vectors depicting the gas molecules is followed in physical space,

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“…17,18 In a recent work, 19 we proposed an efficient method to use the LJ intermolecular potential in DSMC simulations by obtaining the LJ scattering angle as a polynomial expansion in the non-dimensional collision parameters. The model is briefly discussed and summarized in Sec.…”

Section: Introductionmentioning

confidence: 99%

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

Venkattraman

Alexeenko

2012

Physics of Fluids

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A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS model's performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations.

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Solution to the Boltzmann kinetic equation for high-speed flows

Cited by 96 publications

References 4 publications

Kinetic theory aspects of non-equilibrium liquid-vapor flows

Kinetic theory aspects of non-equilibrium liquid-vapor flows

Programming and modelling environment for studies of gas flows in micro- and nanostructures based on solving the Boltzmann equation

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

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