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

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