Diffuse interface models for two-phase flows in artificial compressibility approach

Abstract

We present an approach to numerical simulation of two-phase flows in the so-called one-fluid formulation, combining the Entropically Damped Artificial Compressibility (EDAC) method for flow solution and a chosen variant of the Phase Field Method (PFM) that belongs to a wider family of the Diffuse Interface (DI) methods of interface capturing. The resulting governing equations express a set of conservation laws and are of the advection-diffusion type, convenient in numerical handling. These equations, rewritten in the semi-discrete form, can be efficiently solved on parallel devices using the method of lines. We applied the conservative finite difference method for the spatial discretisation and a variant of the Runge-Kutta method to advance the solution in time. The results presented in this work contain the analysis of spurious currents in the case of stationary droplet together with the pressure jump across its surface, as well as the deformation of a droplet subjected to the laminar Couette flow. The presented EDAC-DI approach, offering very high computational efficiency, gives results comparable to other well-established methods for the simulations of the interfacial flows.