Pairwise Wave Interactions in Ideal Polytropic Gases

Geng Chen, Erik E. Endres, Helge Kristian Jenssen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider the problem of resolving all pairwise interactions of shock waves, contact waves, and rarefaction waves in the one-dimensional flow of an ideal polytropic gas. Here, resolving an interaction means to determine the types of the three outgoing (backward, contact, and forward) waves in the Riemann problem defined by the extreme left and right states of the two incoming waves, together with possible vacuum formation. This problem has been considered by several authors and turns out to be surprisingly involved. For each type of interaction (head-on, involving a contact, or overtaking) the outcome depends on the strengths of the incoming waves. In the case of overtaking waves the type of the reflected wave also depends on the value of the adiabatic constant. Our analysis provides a complete breakdown and gives the exact outcome of each interaction.

Original languageEnglish (US)
Pages (from-to)787-836
Number of pages50
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Jun 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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