Solutions of a nonhyperbolic pair of balance laws

Michael Sever*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, non-hyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome, however, by introducing an alternative "solution" satisfying both components of the initial data and an approximate form of a corresponding linearized system.

Original languageEnglish
Pages (from-to)37-58
Number of pages22
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume39
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

  • Incompressible two-fluid flow
  • Nonhyperbolic balance laws

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