We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few).

我们提出了一个完全欧拉混合浸入边界/相场模型来模拟任何任意几何形状上的润湿和接触线运动。固体壁用体积惩罚鬼细胞浸入边界描述，而两种流体之间的界面则用扩散界面方法描述。复杂壁上的接触线运动通过动量方程中的滑移速度和 Cahn-Hilliard 模型的阶参数的静态/动态接触角条件指定。这种组合需要准确计算标量阶参数和速度分量的法向和切向梯度。然而，本算法需要计算平均权重和其他几何变量作为预处理步骤。手稿中报告了几项验证测试，连同在具有不同接触角和滑移长度的正弦壁上扩散的液滴以及在球体上扩散的球形液滴的二维模拟，表明所提出的算法能够处理任何复杂壁上的三相接触线运动。该算法的欧拉特征促进了实现，并提供了直接且潜在的高度可扩展的并行化。底层 Navier-Stokes 求解器所采用的并行化也可以有效地用于多相部分。此处提出的程序可直接用于为在复杂几何上演化的任何场变量施加任何类型的边界条件（Neumann、Dirichlet 和混合），使用浸入边界方法建模（例如，对可变形生物膜进行建模，