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 generalization of a model previously studied in the literature, in which the densities and the viscosities of the two phases are allowed to be different. Then, we introduce a finite-difference scheme for the numerical computations and the qualitative validation of the model. In particular, the use of an anti-diffusive second-order scheme for the transport scheme is explained and justified. One of the main physical experiment that we manage to simulate is the one of the spinodal decomposition under shear, but in order to show that the model is relevant in many general situations, we also obtain significant results in three other cases: the driven cavity, the Rayleigh-Taylor instability and the fall of a droplet. (C) 2001 Elsevier Science Ltd. All rights reserved.