| keyword(s) : théorie cinétique – coefficients de transport – mélanges ionisés – diffusion – diffusion thermique – entropie – séries convergentes – plasmas – plasmas ambipolaires – réactions chimiques – système symétrique hyperbolique/parabolique – formes normales – stabilité asymptotique – états d'équilibre – problème de Cauchy – flammes ionisées – calcul de flammes. |
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| Modeling for dissipative ionized reactive gas mixtures |
We investigate macroscopic models of PDE for ionised reactive gas
mixtures and we perform some mathematical studies and numerical
simulations. We obtain the macroscopic equations just like expressions for transport fluxes by using the Enskog expansion of a generalized Boltzmann equation. We then investigate symmetry properties given by the entropy for the coupled system composed with the fluid equations and the Maxwell's equations and we prove local existence and uniqueness of a bounded smooth solution for the Cauchy problem. We next investigate a system modeling ambipolar plasmas where the electron mass is considerd as a parameter. We establish the continuous dependence of global solutions with respect to vanishing electron mass. We finally compute plane and strained ionised flames for hydrogen-air mixture et we obtain classical structures with weak impact of ionisation. |
| english keyword(s) : kinetic theory – transport coefficients – ionized mixture – diffusion – thermal diffusion – entropy – convergent series – plasmas – ambipolar plasmas – chemical reactions – symmetric hyperbolic/parabolic system – normal forms – asymptotic stability – equilibrium state |
