Boundary Layers and Shock Profiles for the Broadwell Model

Boundary Layers and Shock Profiles for the Broadwell Model

We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock pr...

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Main Author: Niclas Bernhoff
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2016/5801728
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spelling doaj-a3681c0665584f34aa69e9b355a05bb82020-11-24T23:31:57ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/58017285801728Boundary Layers and Shock Profiles for the Broadwell ModelNiclas Bernhoff0Department of Mathematics, Karlstad University, 65188 Karlstad, SwedenWe consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.http://dx.doi.org/10.1155/2016/5801728
collection DOAJ
language English
format Article
sources DOAJ
author Niclas Bernhoff
spellingShingle Niclas Bernhoff
Boundary Layers and Shock Profiles for the Broadwell Model
International Journal of Differential Equations
author_facet Niclas Bernhoff
author_sort Niclas Bernhoff
title Boundary Layers and Shock Profiles for the Broadwell Model
title_short Boundary Layers and Shock Profiles for the Broadwell Model
title_full Boundary Layers and Shock Profiles for the Broadwell Model
title_fullStr Boundary Layers and Shock Profiles for the Broadwell Model
title_full_unstemmed Boundary Layers and Shock Profiles for the Broadwell Model
title_sort boundary layers and shock profiles for the broadwell model
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2016-01-01
description We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.
url http://dx.doi.org/10.1155/2016/5801728
work_keys_str_mv AT niclasbernhoff boundarylayersandshockprofilesforthebroadwellmodel
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