12 research outputs found
Large amplitude problem of BGK model: Relaxation to quadratic nonlinearity
Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann
equation which is widely used in place of the Boltzmann equation for the
simulation of various kinetic flow problems. In this work, we study the
asymptotic stability of the BGK model when the initial data is not necessarily
close to the global equilibrium pointwisely. Due to the highly nonlinear
structure of the relaxation operator, the argument developed to derive the
bootstrap estimate for the Boltzmann equation leads to a weaker estimate in the
case of the BGK model, which does not exclude the possible blow-up of the
perturbation. To overcome this issue, we carry out a refined analysis of the
macroscopic fields to guarantee that the system transits from a highly
nonlinear regime into a quadratic nonlinear regime after a long but finite
time, in which the highly nonlinear perturbative term relaxes to essentially
quadratic nonlinearity.Comment: 34 pages, 1 figure
The BGK equation as the limit of an particle system
The spatially homogeneous BGK equation is obtained as the limit if a model of
a many particle system, similar to Mark Kac's charicature of the spatially
homogeneous Boltzmann equation.Comment: Minor corrections and modifications only. This version is essentially
the same as the published pape
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal