Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 104, pp. 1-18.
Title: From discrete Boltzmann equation to compressible
linearized Euler equations
Author: Abdelghani Bellouquid (Politecnico of Torino, Italy)
Abstract:
This paper concerns the asymptotic analysis of the linearized
Euler limit for a general discrete velocity model of the
Boltzmann equation. This is done for any dimension of the physical
space, for densities which remain in a suitable small
neighbourhood of global Maxwellians. Providing that the initial
fluctuations are smooth, the scaled solutions of discrete
Boltzmann equation are shown to have fluctuations that locally
in time converge weakly to a limit governed by a solution
of linearized Euler equations. The weak limit becomes strong
when the initial fluctuations converge to appropriate initial data.
As applications, the two-dimensional 8-velocity model and the
one-dimensional Broadwell model are analyzed in detail.
Submitted February 5, 2004. Published September 8, 2004.
Math Subject Classifications: 58J05, 53C21.
Key Words: Discrete Boltzmann equation; kinetic theory;
asymptotic theory; compressible Euler; Broadwell model.