A weakly compressible, diffuse interface model of two-phase flows: Numerical development and validation

Abstract

We present an approach to simulation of low speed, two-phase interfacial flows. It utilises the diffuse-interface method, based on the so-called conservative Allen–Cahn equation with some further modifications. The flow description allows for weak density variations (weak compressibility) as a computationally efficient treatment of incompressible flow regime. The proposed model conserves mass and momentum. The pressure field evolves according to the energy conservation law for inviscid fluids, expressed in primitive variables. The assumption of weak compressibility leads to some modelling and numerical issues related to the need of unique interface region identification required by the one-fluid formulation. We propose a successful and efficient remedy to this problem which, importantly, is independent of the Mach number. To numerically solve the governing equations we use the classical finite volume method and explicit time integration. This makes the presented strategy easy to implement in existing numerical codes and allows for efficient execution of the simulations using parallel computing devices. The spatial discretisation needs some special care to preserve the simplicity without impairing the fundamental physical consistency. We propose the values of tunable model parameters resulting in an universal approach, suitable for a wide variety of interfacial flows. The approach is validated both qualitatively and quantitatively for a selection of well known benchmark cases in two- and three-dimensional set-ups. High computational efficiency is obtained with simple programming techniques when the code is executed on multicore CPU.