Numerical study of viscoelastic mixtures through a Cahn-Hilliard flow model
Résumé
In this paper we are concerned with the numerical study of viscoelastic diphasic flows. We first propose a complete model and give some formal justifications including the case where both or one phase is a non-Newtonian one. Then, we have implemented a numerical method taking into account the lagrangian transport in the resolution of the extra-stress equation of Oldroyd type. We describe this fully-practical method and prove its stability so that one can perform long-time numerical simulations. Several significant tests (channel under shear, filling of tanks, breakup of jets...) illustrate the pertinency of the model and of the numerical method. We show that the results are in accordance with the various qualitative behaviors observed in physical experiments.