A unified finite volume framework for phase‐field simulations of an arbitrary number of fluid phases

Abstract

While the phase-field methodology is widely adopted for simulating two-phase flows, the simulation of an arbitrary number ( N ≥ 2) of fluid phases at physical fidelity is non-trivial and requires special attention concerning mathematical modelling, numerical discretization, and solution algorithm. We present our most recent work with a focus on validation for multiple immiscible, incompressible, and isothermal phases, enhancing further our library for diffuse interface phase-field interface capturing methods in OpenFOAM (FOAM-extend 4.0/4.1). The phase-field method is an energetic variational formulation based on the work of Cahn and Hilliard where the interface is composed of a physical diffuse layer resembling realistic interfaces. The evolution of the phases is then governed by the minimization of the free energy of the system. The accuracy of the method is demonstrated for a number of test problems, including a floating liquid lens, bubble rise in two stratified layers, and drop impact onto thin