In the following sections the drift flux model and the two fluid model are explained.
In a two fluid model, a set of conservative equations is used for each fluid (phase).
Some authors assume isothermal analysis , ,  or adiabatic conditions  from the wall of the pipe, other authors used only one mixture energy conservative equation in spite of develop an hydraulic two fluid model .
In addition to the equation system, the solution of a two fluid model is harder to found than the one of the drift flux model because there are more coupled equations.
A numerical analysis of the two fluid model near ill posedness was made by .