Numerical approximation of Knudsen layer for the Euler-Poisson system

Charles, Frédérique; Vauchelet, Nicolas; Besse, Christophe; Goudon, Thierry; Lacroix–Violet, Ingrid; Dudon, Jean-Paul; Navoret, Laurent

doi:10.1051/proc/2011020

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Remark 34 the Discussion Of Knudsen Layers And Their Numer1

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2011

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“…The mathematical analysis of such matching condition is highly delicate, and we refer to the breakthrough of A. Vasseur concerning nonlinear scalar conservation laws [56]. We shall go back to this problem elsewhere and we will also consider the effect of a coupling with an electric potential [19]. We also point out that our approach can be improved by using a more involved approximation of the half-space problem, while here the computations are simply based on the Maxwell approximation: the iterative procedure described in [33] looks quite appealing for this purpose.…”

Section: Remark 34 the Discussion Of Knudsen Layers And Their Numermentioning

confidence: 99%

Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

et al. 2011

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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.

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Section: Remark 34 the Discussion Of Knudsen Layers And Their Numermentioning

confidence: 99%