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Entropy inequalities for evaporation/condensation problem in rarefied gas dynamics.

Alexey Heintz (Institutionen för matematik, Matematik/Tillämpad matematik) ; Bobylev Alexander ; Richards Grzhibovskis (Institutionen för matematik, Matematik/Tillämpad matematik)
Journal of statistical physics (0022-4715). Vol. 102 (2001), 5-6, p. 1151–1176.
[Artikel, refereegranskad vetenskaplig]

The present paper is devoted mainly to the half space problem for stationary Boltzmann-type equations. Using only conservation laws and the Boltzmann H-theorem we derive an inequality for unknown constant fluxes of mass, energy, and momentum. This inequality is expressed in terms of three parameters (pressure p, temperature T and the Mach number M) of the asymptotic Maxwellian at infinity. Geometrically the inequality describes a “physical” domain with positive entropy production in the 3-d space of the parameters. The domain appears to be qualitatively different for evaporation and condensation problems. We show that for given M, the curve p=p(M), T=T(M) of maximal entropy production practically coincides with the experimental evaporation curve obtained by Sone et al. on the basis of numerical solutions of BGK equation. Similar consideration for the condensation problem is also in qualitative agreement with known numerical results.



Denna post skapades 2015-07-06.
CPL Pubid: 219446

 

Institutioner (Chalmers)

Institutionen för matematik, Matematik/Tillämpad matematik (1987-2001)

Ämnesområden

Matematisk analys

Chalmers infrastruktur