This is a provisionnal version, working document : please send any comments to Sylvie Malardel, Jean-FranÃ§ois Geleyn or Pierre BÃ©nard (you can use the forum linked to this article).
In the paper, the authors (Sylvie Malardel, Jean-FranÃ§ois Geleyn and Pierre BÃ©nard) consider a multiphase system of n+1 componants. They study the content of an eulerian (geometric or fixed) volume V. At a given time t, the total mass of mixure contained in the volum V is m and the mass of the species t contained in the volume V is mt.
They also work at two different scales :
– the scale of the Navier-Stokes equation, the scale of the continuum : "local" scale
– a larger scale : the scale of the parametrisation in the physic part of the model or the scale represented by the troncated equations of a numerical model.
This paper gives only continuous formulation of the equations. The discretisation problem should be treated separately.