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Volume 3, Issue 5
Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

Christophe Besse, Saja Borghol, Thierry Goudon, Ingrid Lacroix-Violet & Jean-Paul Dudon

Adv. Appl. Math. Mech., 3 (2011), pp. 519-561.

Published online: 2011-03

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  • Abstract

We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

  • Keywords

Hydrodynamic regimes, Knudsen layer, finite volume scheme, initial-boundary value problems for conservation laws, Evaporation-condensation problem.

  • AMS Subject Headings

35L65, 35Q35, 82C80, 82C40, 76M12, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-519, author = {Christophe and Besse and and 20332 and and Christophe Besse and Saja and Borghol and and 20333 and and Saja Borghol and Thierry and Goudon and and 20334 and and Thierry Goudon and Ingrid and Lacroix-Violet and and 20335 and and Ingrid Lacroix-Violet and Jean-Paul and Dudon and and 20336 and and Jean-Paul Dudon}, title = {Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {5}, pages = {519--561}, abstract = {

We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1041}, url = {http://global-sci.org/intro/article_detail/aamm/181.html} }
TY - JOUR T1 - Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes AU - Besse , Christophe AU - Borghol , Saja AU - Goudon , Thierry AU - Lacroix-Violet , Ingrid AU - Dudon , Jean-Paul JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 519 EP - 561 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1041 UR - https://global-sci.org/intro/article_detail/aamm/181.html KW - Hydrodynamic regimes, Knudsen layer, finite volume scheme, initial-boundary value problems for conservation laws, Evaporation-condensation problem. AB -

We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

Christophe Besse, Saja Borghol, Thierry Goudon, Ingrid Lacroix-Violet & Jean-Paul Dudon. (1970). Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes. Advances in Applied Mathematics and Mechanics. 3 (5). 519-561. doi:10.4208/aamm.10-m1041
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