A simple method for compressible multiphase mixtures and interfaces

Nikolai Andrianov, Richard Saurel, Gerald Warnecke

Research output: Contribution to journalArticleResearchpeer-review

38 Citations (Scopus)


We develop a Godunov-type scheme for a non-conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non-equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.). Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non-conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions.

Original languageEnglish
Pages (from-to)109-131
Number of pages23
JournalInternational Journal for Numerical Methods in Fluids
Issue number2
Publication statusPublished - 20 Jan 2003
Externally publishedYes


  • Godunov-type scheme
  • Hyperbolic model
  • Multiphase flow

Programme Area

  • Programme Area 3: Energy Resources


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