Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier-Stokes-Cahn-Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche's method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor-Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

翻译：二元流体流动可通过Navier-Stokes-Cahn-Hilliard方程建模，该方程采用扩散界面表征流体组分间的边界。扩散界面模型能够处理二元流体界面的复杂几何形态及拓扑变化。本文提出一种浸入式等几何分析框架，用于在具有几何复杂外部二元流体边界的域上求解Navier-Stokes-Cahn-Hilliard方程。采用最优正则性B样条实现了计算高效的高阶方法。该框架的关键特征包括：切向速度分量的广义Navier滑移边界条件、对流不可穿透边界条件的Nitsche方法，以及用于保证稳定性的骨架罚与虚拟罚。采用二元流体Taylor-Couette流动进行基准测试。多孔介质模拟展示了该浸入式等几何分析框架在复杂几何中模拟二元流体破裂与聚并等复杂流动现象的能力。