Acta Applicandae Mathematicae

, Volume 129, Issue 1, pp 1–21 | Cite as

Modelling of an Homogeneous Equilibrium Mixture Model (HEM)

  • A. Bernard-ChampmartinEmail author
  • O. Poujade
  • J. Mathiaud
  • J.-M. Ghidaglia


We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented.


Mixture model Drift closure Two phase flows Darcy law 

Mathematics Subject Classification (2010)

76T10 76N99 65Z05 65M06 41A60 



A.B.C. acknowledges partial support of ANR CBDif-Fr, Collective behaviour & diffusion: mathematical models and simulations ANR-08-BLAN-0333-01.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • A. Bernard-Champmartin
    • 1
    • 2
    • 3
    • 4
    Email author
  • O. Poujade
    • 1
  • J. Mathiaud
    • 1
    • 2
  • J.-M. Ghidaglia
    • 2
  1. 1.CEA, DAM, DIFArpajonFrance
  2. 2.CMLA, ENS Cachan, CNRS, UniverSudCachanFrance
  3. 3.INRIA Sophia Antipolis MéditerranéeSophia Antipolis CedexFrance
  4. 4.LRC MESO, ENS Cachan/CEA, DAM, DIFCachan CedexFrance

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