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.

在这项工作中，我们提出了一种新的相场模型，用于模拟准确、保守、有界和鲁棒的两相流。所提出的模型保留了每个相的质量，并导致体积分数的有界传输。我们展示了液滴平流和剪切流中液滴的典型测试用例的结果，与常用的保守相场方法相比，精度有了显着提高。

此外，所提出的模型施加了限制较少的 Courant-Friedrichs-Lewy 条件，因此与其他保守相场模型相比，成本更低。我们还提出了对表面张力计算的改进，并表明所提出的改进显着降低了界面处虚假速度的大小。

我们还为所提出的相场模型推导出了一致且保守的动量传输方程，并表明当与一致动量传输方程耦合时，所提出的模型会导致动能的离散守恒，这是不可压缩数值稳定性的充分条件在没有耗散机制的情况下流动。为了说明该方法在模拟高密度比湍流两相流中的鲁棒性，我们提出了有限和无限雷诺数下的高密度比载液滴各向同性湍流的数值模拟。