Consistent, energy-conserving momentum transport for simulations of two-phase flows using the phase field equations

TL;DR

This paper introduces an energy-conserving, consistent momentum transport scheme for two-phase flow simulations using phase field methods, improving accuracy and robustness in high Reynolds number and high density ratio scenarios.

Contribution

The authors develop a novel momentum transport scheme that accounts for phase field mass flux and employs non-dissipative discretization, enhancing simulation accuracy and robustness.

Findings

Improved accuracy in turbulent two-phase flow simulations.

Reduced spurious currents in surface tension calculations.

Enhanced robustness in high Reynolds number flows.

Abstract

Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving momentum transport scheme in the context of a second order mass-conserving phase field method. This is achieved by (1) accounting for the mass flux associated with the right-hand-side of the phase field equation in the convective flux of the conservative form of the momentum transport equation---a correction absent in previous phase field simulations (2) utilization of non-dissipative spatial discretization. We demonstrate accuracy and robustness improvements from our proposed scheme via numerical tests, including a turbulent case of a water jet subject to air cross-flow. Our proposed modifications to the momentum transport equation can be quite readily extended to general conservative phase field methods. Additionally, in the framework of this phase field method, we present a free energy-based surface tension force calculation scheme. This scheme, which significantly reduces spurious currents, is based on a general paradigm that can also be extended to other two-phase flow methods.