Some aspects of the modeling at different scales of multiphase flows

We present the various levels of possible modeling for multiphase flows: coupling of fluid equations in different domains with a free boundary; coupling (in the same domain) of a fluid equation and a kinetic (Vlasov or Vlasov-Boltzmann) equation; coupling (in the same domain) of two (or more) fluid equations. We briefly present the mathematical results relative to the passage from one of these approaches to another approach, and we give some ideas of how to use those different models on a specific practical example. (C) 2009 Elsevier B.V. All rights reserved.