Abstract In this study, we present a novel Cahn–Hilliard–Navier–Stokes (CHNS) system with a nonstandard variable mobility for two-phase incompressible fluid flow. Unlike the classical constant mobility, the developed variable mobility has decreasing values nearby the interface and increasing values away from the interface, which minimizes the dynamics of the Cahn–Hilliard (CH) model nearby the interface. An unconditionally stable convex splitting method is used to solve the CH equation and the projection method is used to solve the NS equation. As benchmark tests, the Rayleigh–Taylor instability, drop deformation, and rising bubble are performed to show the accuracy and practicability of the proposed model. The computational results indicate that the proposed model accurately captures the interfacial position and keeps the interface region from being too much distorted.

中文翻译：

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具有非标准可变流动性的两相不可压缩流体流动的新型 Cahn-Hilliard-Navier-Stokes 模型

摘要 在这项研究中，我们提出了一种新型 Cahn-Hilliard-Navier-Stokes (CHNS) 系统，该系统具有用于两相不可压缩流体流动的非标准可变流动性。与经典的恒定迁移率不同，发达的可变迁移率在界面附近具有递减值并在远离界面时递增，这使界面附近的 Cahn-Hilliard (CH) 模型的动态最小化。CH方程采用无条件稳定凸分裂法求解，NS方程采用投影法求解。作为基准测试，进行瑞利-泰勒不稳定性、液滴变形和气泡上升，以显示所提出模型的准确性和实用性。