Berlin 2015 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 17: Poster (permanent Di-Do)
MP 17.3: Poster
Dienstag, 17. März 2015, 09:30–18:00, HFT-FT 101
Multiple-scale expansions for the Boltzmann equation — •Olga Chekmareva1 and Igor Chekmarev2 — 1Aachen, Germany — 2Aachen, Germany
The nondimensional Boltzmann equation is considered for small Knudsen number. The aim is to represent the solution by the first term of the asymptotic expansion that provides a good approximation for all times of interest. In this case each term in expansion must be a small correction to the preceding terms over long time interval. Thus, it is necessary not only to define the first approximations but examine the higher terms and eliminate the sources of singularities at each step of asymptotic procedure. To attain results we use the multiple-scale technique. Such approach applied to the Boltzmann equation in the limit of small Knudsen reduces to the regular gas-dynamic-type relations for the leading terms and determines the limits of their application. In particular, those equations define the damping and the dispersion of the sound wave. From other hand, the Navier-Stokes equations in the rare gas case contain itself a small parameter and can lead to singular solutions. It is shown the asymptotic equivalence of the Boltzmann equation and the Navier-Stokes system within the framework of the used models.