Journal ArticleDOI
Asymptotic expansions of solutions for the Boltzmann equation
Reads0
Chats0
TLDR
In this article, a modified version of the Hilbert and Chapman-Enskog expansions is developed, which combines the best features of the two expansions and results in nonlinear and linearized Navier-Stokes equations only and is valid in the above-mentioned regimes.Abstract:
The Hilbert and Chapman-Enskog expansions approximate solutions of the Boltzmann equation, but each has some disadvantages: The Hilbert expansion, which results in nonlinear and linearized Euler equations, is invalid for weak shocks, weak boundary layers and long time asymptotics. The Chapman-Enskog expansion results in nonlinear Euler then Navier-Stokes then Burnett and super-Burnett equations. Navier-Stokes is correct for weak shocks, weak boundary layers and long time asymptotics, but the Burnett equations have spurious high order dispersive effects. In this paper a modified expansion is developed, which combines the best features of the two expansions. It results in nonlinear and linearized Navier-Stokes equations only and is valid in the above-mentioned regimes.read more
Citations
More filters
Journal ArticleDOI
Stationary solutions of the linearized Boltzmann equation in a half-space
TL;DR: In this paper, the authors extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential, and obtain asymptotic behavior for hard as well as soft potentials.
Journal ArticleDOI
Binary Fluids with Long Range Segregating Interaction. I: Derivation of Kinetic and Hydrodynamic Equations
TL;DR: In this article, the evolution of a two component fluid consisting of "blue" and "red" particles which interact via strong short range (hard core) and weak long range pair potentials was studied.
Journal ArticleDOI
Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations
TL;DR: In this article, the evolution of a two component fluid consisting of ''blue'' and ''red'' particles which interact via strong short range (hard core) and weak long range pair potentials is studied.
Journal ArticleDOI
Knudsen layers from a computational viewpoint
TL;DR: In this paper, the boundary layer equations arising in the kinetic theory of gases are solved by a simple variational procedure inspired from Pomraning's computations for radiative transfer problems.
Journal ArticleDOI
The Milne problem for the radiative transfer equations (with frequency dependence)
TL;DR: In this paper, the authors study the stationary frequency dependent transport equation with dependance en frequence and derive the asymptotic behavior of f and T for x large, when a(>, T) is of the special form a(> T) = tr(M)k(T).
References
More filters
Book
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
TL;DR: Quasi-linear Hyperbolic Equations Conservation Laws Single Conservation Laws The Decay of Solutions as t Tends to infinity Hypothesis of conservation laws Pairs of Conservation Laws as mentioned in this paper.
Journal ArticleDOI
Theory and Application of the Boltzmann Equation
Carlo Cercignani,A. S. Berman +1 more
Book ChapterDOI
Principles of the Kinetic Theory of Gases
TL;DR: In this article, the subject of the kinetic theory of gases is considered to be coextensive with the theory of the Boltzmann equation, and only the original equation of Maxwell and of Boltzman for classical point molecules and short range forces are considered.
Book
Grundzuge Einer Allgemeinen Theorie Der Linearen Integralgleichungen
TL;DR: In this article, a Funktion K(s, t) heise der Kern der Integralgleichungen, i.e., the bestimmende Funktion of a reelle Veranderlichen.
Related Papers (5)
Asymptotic expansion of the solution of navier-stokes equation in tube structure and partial asymptotic decomposition of the domain
Asymptotic analysis of the linearized Navier-Stokes equations in a general 2D domain
Roger Temam,Xiaoming Wang +1 more