A theoretical and numerical model for the study of incompressible mixture flows

In this paper we give a complete derivation of a new model for the study of incompressible mixture flows. The equations introduced are a generalizatio n of a model previously studied in the literature, in which the densities a nd the viscosities of the two phases are allowed to be different. Then, we introduce a finite-difference scheme for the numerical computation s and the qualitative validation of the model. In particular, the use of an anti-diffusive second-order scheme for the transport scheme is explained a nd justified. One of the main physical experiment that we manage to simulate is the one o f the spinodal decomposition under shear, but in order to show that the mod el is relevant in many general situations, we also obtain significant resul ts in three other cases: the driven cavity, the Rayleigh-Taylor instability and the fall of a droplet. (C) 2001 Elsevier Science Ltd. All rights reser ved.