Some Applications of the Generalized Boltzmann Physical Kinetics

Alexeev, Boris V.

doi:10.1016/b978-044451582-7/50032-1

Cited by 27 publications

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“…Despite the problems observed with equations (12) and (19), kinetic equation (1) and others of that type do admit an H-theorem [3,4]. In the following sections we demonstrate, using a scaling analysis, that the problematic terms do not actually belong to the standard vanishing Knudsen number regime.…”

Section: The Thermodynamic and Mechanical Inconsistenciesmentioning

confidence: 98%

“…This view of a scale difference between the molecular and the macroscopic/hydrodynamic interpretations of the position variable is shared by a number of researchers [3,11,15,[20][21][22].…”

Section: B Resolving the Spatial And Temporal Scaling Problemmentioning

confidence: 99%

“…In the subsequent continuum-fluid set of partial differential equations, a spatial stochastic term in the kinetic model results in an additional mass or volume diffusive term. This term has always been a source of controversy (see, for example, a review in [3]). Paradoxically, however, when applied to some non-continuum flows it appears that a diffusive volume-mass model can capture some non-continuum flow behaviour and resolve some observed paradoxes [3,[6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…Some criticisms of the original Boltzmann model have led to various proposals for modifications, for example, incorporating a spatial stochastic term [3][4][5]. In the subsequent continuum-fluid set of partial differential equations, a spatial stochastic term in the kinetic model results in an additional mass or volume diffusive term.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Dadzie

Reese

2012

Phys. Rev. E

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This version is available at https://strathprints.strath.ac.uk/39217/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.

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Section: The Thermodynamic and Mechanical Inconsistenciesmentioning

confidence: 98%

“…This view of a scale difference between the molecular and the macroscopic/hydrodynamic interpretations of the position variable is shared by a number of researchers [3,11,15,[20][21][22].…”

Section: B Resolving the Spatial And Temporal Scaling Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Dadzie

Reese

2012

Phys. Rev. E

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“…NLE include quantum hydrodynamics of Schrödinger-Madelung as a deep particular case [15] and can be applied in the frame of the unified theory from the atom scale to the Universe evolution. (4) The choice of the non-local parameter needs special consideration [19][20][21][22]. The system of equations (3.2)-(3.4) convert in the system of quantum hydrodynamic equations by the suitable choice of the non-local parameter τ .…”

Section: Investigation Of the Soliton Movement Under Action Of The Somentioning

confidence: 99%

To the Non-Local Theory of Cold Nuclear Fusion

2015

Unified Non-Local Theory of Transport Processes

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Quasi‐gasdynamic numerical algorithm for gas flow simulations

Елизарова

Khokhlov

Sheretov

2007

Numerical Methods in Fluids

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SUMMARYThe quasi-gasdynamic equation system and the numerical algorithm for non-stationary viscous gasdynamic flow calculations are presented. The quasi-gasdynamic equation system generalizes the Navier-Stokes equations and differs from it by the additional dissipative terms. The numerical examples are presented. QUASI-GASDYNAMIC EQUATIONSThe paper is devoted to the contemporary mathematical model for gas flows and to the related numerical methods for flow simulations. The mathematical model generalizes the Navier-Stokes (NS) system of equations. This model is different from the NS system in additional dissipative terms with a small parameter in . The new model is named the quasi-gasdynamic (QGD) system of equations. The first variant of the QGD system was presented in [1] and developed later in, e.g. [2][3][4][5]. The QGD system has a form of the conservation laws and in common notations is expressed as * *t +div j m = 0 (1)

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Some Applications of the Generalized Boltzmann Physical Kinetics

Cited by 27 publications

References 0 publications

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

To the Non-Local Theory of Cold Nuclear Fusion

Quasi‐gasdynamic numerical algorithm for gas flow simulations

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