Two-phase flows - Second-order schemes and boundary conditions

A second-order numerical method suitable to unstructured grids is developed for the solution of two-phase flow equations. A number of assumptions are introduced, justified on physical grounds, when the dispersed phase concentration is low; their effect is to change the mathematical nature of the system of equations. The new numerical method put forward builds on Van Leer's original ideas. The solution of two Riemann problems is involved: one for the gas phase and a second for the dispersed phase. The method is first tested on a one-dimensional case, with excellent results; it is then generalized to two dimensions