Abstract. The aim of this paper is to describe some numerical aspects linked to incompressible three-phase flow simulations, thanks to Cahn-Hilliard type model. The numerical capture of transfer phenomenon in the neighborhood of the interface require a mesh thickness which become crippling in the case where it is applied to the whole computational domain. This suggests the use of a local refinement method which allows to dynamically focus on problematic areas. The notion of refinement pattern, introduced for Lagrange finite elements, allows to build a conceptual hierarchy of nested conformal approximation spaces which is then used to implement the so-called CHARMS local refinement methods. Properties of these methods are proved ensuring in particular the conformity of approximation spaces at every time of simulations. Furthermore, the multilevel structure obtained by this method, is used to construct multigrid preconditioners. Finally, after a validation on a model problem, the performance of the whole method is illustrated on an example of a liquid lens spreading between two stratified fluids. Résumé. L’objectif de l’article est de décrire certains aspects numériques liés à la simulation d’écoulements incompressibles à trois phases non miscibles, à l’aide de modèles à interfaces diffuses de type Cahn-Hilliard. La capture numérique des phénomènes de transfert au voisinage des interfaces requiert

Object oriented MATLAB software components that have been developed for and used in instruction of computational structural engineering are described. It is shown that the object orientation leads to elegant and concise implementations, which helps promote learning and understanding of the subject at the level of the algorithms.

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