Wave structure induced by fluid-dynamic limits in the Broadwell model

Athanasios Tzavaras*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Consider the fluid-dynamic limit problem for the Broadwell system of the kinetic theory of gases, for Maxwellian Riemann initial data. The formal limit is the Riemann problem for a pair of conservation laws and is invariant under dilations of coordinates. The approach of self-similar fluid-dynamic limits consists in replacing the mean free path in the Broadwell model so that the resulting problem preserves the invariance under dilations. The limiting procedure was justified in [ST]. Here, we study the structure of the emerging solutions. We show that they consist of two wave fans separated by a constant state. Each wave fan is associated with one of the characteristic fields and is either a rarefaction wave or a shock wave. The shocks satisfy the Lax shock conditions and have the internal structure of a Broadwell shock profile.

Original languageEnglish (US)
Pages (from-to)361-387
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume127
Issue number4
DOIs
StatePublished - Dec 1 1994

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'Wave structure induced by fluid-dynamic limits in the Broadwell model'. Together they form a unique fingerprint.

Cite this