Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation
Abstract
It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwelllike kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of monoenergetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified twodimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a threedimensional configuration. Finally, the case of nonelastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics ofmore »
 Authors:
 University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F33400 Talence (France)
 Publication Date:
 OSTI Identifier:
 22598911
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; ACCIDENTS; APPROXIMATIONS; BEAMS; BOLTZMANN EQUATION; BOUNDARY CONDITIONS; CONFIGURATION; ELASTIC SCATTERING; GAS FLOW; INCIDENCE ANGLE; KERNELS; MORPHOLOGY; NANOSTRUCTURES; NUMERICAL SOLUTION; ROUGHNESS; THREEDIMENSIONAL CALCULATIONS; TWODIMENSIONAL CALCULATIONS; WALLS
Citation Formats
Brull, S., Email: Stephane.Brull@math.ubordeaux.fr, Charrier, P., Email: Pierre.Charrier@math.ubordeaux.fr, and Mieussens, L., Email: Luc.Mieussens@math.ubordeaux.fr. Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation. United States: N. p., 2016.
Web. doi:10.1063/1.4960024.
Brull, S., Email: Stephane.Brull@math.ubordeaux.fr, Charrier, P., Email: Pierre.Charrier@math.ubordeaux.fr, & Mieussens, L., Email: Luc.Mieussens@math.ubordeaux.fr. Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation. United States. doi:10.1063/1.4960024.
Brull, S., Email: Stephane.Brull@math.ubordeaux.fr, Charrier, P., Email: Pierre.Charrier@math.ubordeaux.fr, and Mieussens, L., Email: Luc.Mieussens@math.ubordeaux.fr. 2016.
"Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation". United States.
doi:10.1063/1.4960024.
@article{osti_22598911,
title = {Nanoscale roughness effect on Maxwelllike boundary conditions for the Boltzmann equation},
author = {Brull, S., Email: Stephane.Brull@math.ubordeaux.fr and Charrier, P., Email: Pierre.Charrier@math.ubordeaux.fr and Mieussens, L., Email: Luc.Mieussens@math.ubordeaux.fr},
abstractNote = {It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwelllike kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of monoenergetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified twodimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a threedimensional configuration. Finally, the case of nonelastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gassurface interaction, at a reasonable computing cost, to improve kinetic simulations of micro and nanoflows.},
doi = {10.1063/1.4960024},
journal = {Physics of Fluids},
number = 8,
volume = 28,
place = {United States},
year = 2016,
month = 8
}

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