The purpose of the course is to provide state-of-the-art 
information on physical modeling and numerical simulation 
of multifluid flows. After reviewing the different 
theoretical modeling of miscible and unmiscible fluid 
flows, emphasis is given to the Lagrangian, Eulerian or 
mixed numerical approaches currently available in 
literature. Lectures are then dedicated to the three main 
techniques commonly used to describe and track the fluid 
interface between unmiscible fluids: the Level Set Method 
(LSM), implicitly based on the zero level of a smooth 
function; the Interface Tracking Method (IFT), where the 
evolution of the interface is treated explicitly and the 
Volume of Fluid (VOF), the algebraic counterpart to the 
IFT method, where the algebraic evolution of a color 
function C is studied and after the interface 
reconstructed from it. When additional flow modeling is 
required, additional complications arise, in particular 
the delicate LES -VOF coupling needed to deal with 
turbulent gas-liquid flow interaction is discussed. 
Finally, typical examples of complex flows are then 
proposed illustrating basic situations and industrial 
applications.