Accurate conservative diffuse-interface method for the simulation of two-phase flows

We present a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and stable. The proposed model conserves the volume/mass of each of the phases, and results in bounded transport of the volume fraction. We present results from the canonical test cases of a drop advection and a drop in a shear flow, showing the improvement in the accuracy over the commonly used second-order conservative phase-field method. Furthermore, we also derive consistent momentum transport equation for the proposed phase-field model and show that the proposed model when coupled with the consistent momentum transport equation results in discrete conservation of kinetic energy, which is a sufficient condition for the numerical stability of incompressible flows, in the absence of dissipative mechanisms. To illustrate the robustness of the method to simulate high-density ratio turbulent two-phase flows, we present the numerical simulation of an infinite Reynolds number high-density ratio droplet-laden isotropic turbulence.

Authors acknowledge Predictive Science Academic Alliance Program III at Stanford University