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, kinetic energy conserving momentum transport scheme in the context of a second order conservative 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 using numerical tests, including a realistic jet in cross-flow attaining turbulent conditions. Our proposed modifications to the momentum transport equation can be readily extended to other conservative phase field methods.

感兴趣的现实两相流问题通常涉及高Re高密度比流动。对此类问题的准确而可靠的模拟需要特殊的处理。在这项工作中，我们在二阶保守相场方法的背景下提出了一种一致的，动能守恒的动量传输方案。这是通过（1）在动量输运方程的保守形式的对流通量中考虑与相场方程右手边相关的质量通量实现的，这是以前的相场模拟中不存在的校正（2）利用非耗散空间离散化。我们使用数值测试证明了我们提出的方案的准确性和鲁棒性，其中包括在横流中达到湍流条件的真实射流。