A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio

Abstract Simulating two-phase flows in realistic industrial-complexity conditions remains an open problem. We present a phase-field method based on the Cahn-Hilliard equation that is able to simulate two-phase flow at high Reynolds number and at large density and viscosity ratios. We employ the entropy-viscosity method (EVM), applied both on the Navier-Stokes equations and phase-field equation, to stabilize the simulation in conjunction with an EVM-based artificial interface compression method (AICM) that maintains the sharpness of the interface. We implement this method based on a hybrid spectral-element/Fourier (SEF) discretization and demonstrate second-order accuracy in time and spectral convergence rate in space for smoothed fabricated solutions. We first test the accuracy and robustness of the stabilized SEF-EVM solver by solving the so-called three-dimensional “LeVeque problem” and compare against other available methods. Subsequently, we simulate a rising air bubble in a water container and find that the method is robust with respect to various parameters of the phase-field formulation. Lastly, we apply the method to simulate the onset and subsequent evolution of an air/oil slug in a long horizontal pipe using realistic parameters and incorporating gravity and surface tension effects. This is a particularly difficult flow to simulate with existing methods in realistic conditions and here we show that the new stabilized phase-field methods yields results in good agreement with the experimental data.