标题： 基于投影的Cahn-Hilliard-Navier-Stokes框架的两相流相场建模 显示英文标题

标题： Phase-Field Modeling of Two-Phase Flows: A Projection-Based Cahn-Hilliard-Navier-Stokes Framework

摘要： 耦合的Cahn-Hilliard和Navier-Stokes（CH-NS）方程为建模具有扩散界面的多相流提供了一个强大的框架，能够模拟液滴破裂、气泡动力学和水动力不稳定性。 这些能力在沸腾传热、微流体、涂层、增材制造和油水分离中至关重要，其中解析流体-流体相互作用是必不可少的。 数值上，CH-NS系统具有挑战性：Cahn-Hilliard方程涉及高阶导数和非线性，而与Navier-Stokes的耦合引入了强烈的双向相互作用。 速度场会输运相场，而演变的界面会改变密度和粘度，并反馈到流动中。 变密度和变粘度系统进一步增加了复杂性，需要准确处理属性对比而不损失稳定性或质量守恒。 为了解决这个问题，我们采用了一种解耦的压力投影方法，在交错网格上使用有限差分和显式欧拉时间步进。 我们的公式扩展了CH-NS系统，以适用于均质和变属性流体，并实现了一致的流体力学-相场耦合。 与经典基准测试（包括气泡上升和Plateau-Taylor不稳定性）进行验证，显示了上升速度、界面形状和不稳定性波长方面的良好一致性。 该框架为多物理场扩展（如传热、相变和电水动力学）建立了可重复的基础，应用于沸腾、液滴操控和电子冷却。 显示英文摘要

摘要： The coupled Cahn-Hilliard and Navier-Stokes (CH-NS) equations provide a powerful framework for modeling multiphase flows with diffuse interfaces, enabling simulations of droplet breakup, bubble dynamics, and hydrodynamic instabilities. These capabilities are vital in boiling heat transfer, microfluidics, coating, additive manufacturing, and oil-water separation, where resolving fluid-fluid interactions is essential. Numerically, the CH-NS system is challenging: the Cahn-Hilliard equation involves higher-order derivatives and nonlinearities, and coupling with Navier-Stokes introduces strong two-way interactions. The velocity field advects the phase field, while the evolving interface alters density and viscosity, feeding back into the flow. Variable-density and variable-viscosity systems further increase complexity, requiring accurate treatment of property contrasts without losing stability or mass conservation. To address this, we employ a decoupled pressure-projection method with finite differences on staggered grids and explicit Euler time stepping. Our formulation extends the CH-NS system to homogeneous and variable-property fluids with consistent hydrodynamic-phase-field coupling. Validation against canonical benchmarks-including bubble rise and Plateau-Taylor instability shows excellent agreement in rise velocity, interface shape, and instability wavelength. This framework establishes a reproducible foundation for multiphysics extensions such as heat transfer, phase change, and electrohydrodynamics in boiling, droplet manipulation, and electronics cooling