Accurate conservative phase-field method for simulation of two-phase flows

TL;DR

This paper introduces a new conservative phase-field model for two-phase flow simulation that improves accuracy, reduces computational cost, and maintains stability, especially in high-density ratio turbulent flows.

Contribution

The paper presents a novel phase-field model that is accurate, conservative, bounded, and less computationally restrictive, with improved surface tension force computation and energy conservation.

Findings

Significant accuracy improvement over existing methods.

Reduced spurious velocities at interfaces.

Successful simulation of high-density ratio turbulent flows.

Abstract

In this work, we propose a novel phase-field model for the simulation of two-phase flows that is accurate, conservative, bounded, and robust. The proposed model conserves the 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 significant improvement in the accuracy over the commonly used conservative phase-field method. Moreover, the proposed model imposes a lesser restrictive Courant-Friedrichs-Lewy condition, and hence, is less expensive compared to other conservative phase-field models. We also propose improvements on computation of surface tension forces and show that the proposed improvement significantly reduces the magnitude of spurious velocities at the interface. We also derive a consistent and conservative 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 in simulating high-density ratio turbulent two-phase flows, we present the numerical simulations of high-density ratio droplet-laden isotropic turbulence at finite and infinite Reynolds numbers.