Numerical transition from Boltzmann to Navier Stokes
Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique42, Avenue Gaspard Coriolis
31057 Toulouse Cedex
Tel : 05 61 19 31 31 - Fax : 05 61 19 30 00
NUMERICAL TRANSITION FROM BOLTZMANN TO NAVIER STOKES
Patrick Le Tallec
(CEREMADE, Université Paris Dauphine)
Friday June 5, 11.00 a.m. CERFACS Conference Room
A gas may be modeled at either the macroscopic or the microscopic scale. When considered at the microscopic level, the gas is treated as a collection of particles characterized by their velocity and position, and is described by the Boltzmann equation, governing the evolution of the velocity distribution of these particles. The characteristic length is then the particle mean free path (average distance covered by a particle between two collisions). For dense gas, this length is very small compared to the macroscopic scale and the numerical solution of Boltzmann equations becomes impossible. We must then abandon this kinetic model in favor of macroscopic fluid dynamics models. There, the gas is considered as a continuous medium and the description is modeled by average variables (typically mass density, average velocity, and temperature) whose evolution is governed either by Euler or by Navier-Stokes equations.
The objective of the talk is to introduce and describe a hierarchy of numerical models and tools (BGK kinetic models, Levermore's moment equations, Chapman Enskog expansions) bridging these two point of views, We will discuss the mathematical consistency, physical relevance and numerical feasibility of these different approaches, concentrating in particular on the treatment of internal energy and/or boundary layers.
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