ABSTRACT
The nonlinear problems are of especial interest in the scientifi c fi eld because most physical systems and phenomena, e.g., chemical reactions, ecology, biomechanics, population growth, and multi-phase or multi-component fl uids phenomena, are nonlinear in nature. The impact of a droplet on a solid surface, nuclear safety, petroleum engineering, and combustion or reaction fl ows are examples of multi-component and multi-phase fl uids. From the point of view of traditional fl uid dynamics, such fl uids are treated as sharp
interfaces on which a set of interfacial balance conditions must be imposed. However, this kind of mathematical modeling and its numerical solutions are diffi cult to develop due to the inherent nonlinearities, topological changes, and the complexity of dealing with unknown moving interfaces present in the fl uids. Phase fi eld models are an alternative approach for solving the interface problems and are used to describe and simulate this kind of fl uids. In a phase fi eld model, the interfaces are described by a mixing energy, so they are implicitly captured in a functional.
