scholarly journals Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations

2017 ◽  
Vol 10 (4) ◽  
pp. 925-955 ◽  
Author(s):  
Niclas Bernhoff ◽  
Keyword(s):  
Boundary Layers ◽  
Kinetic Models ◽  
Kinetic Equations ◽  
Polyatomic Molecules ◽  
Multicomponent Mixtures ◽  
Bimolecular Reactions

scholarly journals Micro-Macro Schemes for Kinetic Equations Including Boundary Layers

2012 ◽  
Vol 34 (6) ◽  
pp. B734-B760 ◽  
Author(s):  
Mohammed Lemou ◽  
Florian Méhats
Keyword(s):  
Boundary Layers ◽  
Kinetic Equations

scholarly journals The Development and Application of a Kinetic Theory for Modelling Dispersed Particle Flows

2021 ◽  
Author(s):  
Mike Reeks
Keyword(s):  
Kinetic Theory ◽  
Boundary Layers ◽  
Kinetic Equations ◽  
Turbulent Boundary Layers ◽  
Collision Kernel ◽  
Gravitational Settling ◽  
Particle Pair ◽  
Particle Flows ◽  
Wall Boundary Conditions ◽  
Near Wall

Abstract This Freeman Scholar article reviews the formulation and application of a kinetic theory for modeling the transport and dispersion of small particles in turbulent gas-flows, highlighting the insights and understanding it has provided and some of the long standing problems in the modeling of dispersed flows it has resolved. The theory has been developed and refined by numerous authors and now forms a rational basis for modeling complex particle laden flows. The formalism and methodology of this approach are discussed and the choice of closure of the kinetic equations involved which ensures realizability and well posedness with exact closure for Gaussian carrier flow fields. The historical development is presented and how single particle kinetic equations resolve the problem of closure of the transport equations for particle mass, momentum and kinetic energy /stress (the so called continuum equations) and the treatment of the dispersed phase as a fluid. The mass fluxes associated with the turbulent aerodynamic driving forces and interfacial stresses are shown to be both dispersive and convective in inhomogeneous turbulence with implications for the build up of particles concentration in near wall turbulent boundary layers and particle pair concentration at small separation. It is shown how this approach deals with the natural wall boundary conditions for a flowing particle suspension and examples are given of partially absorbing surfaces with particle scattering, and gravitational settling; how this approach has revealed the existence of contra gradient diffusion in a developing shear flow and the influence of the turbulence on gravitational settling (the Maxey effect). Particular consideration is given to the general problem of particle transport and deposition in turbulent boundary layers and near wall behavior including particle resuspension. Finally the application of a particle pair formulation for both monodisperse and bidisperse particle flows is reviewed where the differences between the two are compared through the influence of collisions on the particle continuum equations and on the particle collision kernel for the clustering of particles and the degree of random uncorrelated motion (RUM) at the small scales of the turbulence. The inclusion of bidisperse particle suspensions implies the application to polydisperse flows and the evolution of particle size distribution.

scholarly journals A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Casimir Emako ◽  
Farah Kanbar ◽  
Christian Klingenberg ◽  
Min Tang
Keyword(s):  
Distribution Function ◽  
Kinetic Models ◽  
Kinetic Equations ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Schemes

<p style='text-indent:20px;'>In this work we are interested in the stationary preserving property of asymptotic preserving (AP) schemes for kinetic models. We introduce a criterion for AP schemes for kinetic equations to be uniformly stationary preserving (SP). Our key observation is that as long as the Maxwellian of the distribution function can be updated explicitly, such AP schemes are also SP. To illustrate our observation, three different AP schemes for three different kinetic models are considered. Their SP property is proved analytically and tested numerically, which confirms our observations.</p>

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