Asymptotic Expansions of Solutions for the Boltzmann Equation

Russel Caflisch

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)701-725
Number of pages25
JournalTransport Theory and Statistical Physics
Volume16
Issue number4-6
DOIs
StatePublished - Jun 1 1987

Fingerprint

Boltzmann equation
Boltzmann Equation
Asymptotic Expansion
Chapman-Enskog Expansion
Long-time Asymptotics
Burnett equations
expansion
Navier-Stokes
Hilbert
Boundary Layer
Shock
regime
boundary layers
Boundary layers
shock
Euler Equations
Euler equations
Euler
Navier-Stokes Equations
Approximate Solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

Asymptotic Expansions of Solutions for the Boltzmann Equation. / Caflisch, Russel.

In: Transport Theory and Statistical Physics, Vol. 16, No. 4-6, 01.06.1987, p. 701-725.

Research output: Contribution to journalArticle

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