In this paper, we propose a phase field method for the numerical simulations of a moving solid object in two-phase flows. A three-phase Cahn-Hilliard and Navier-Stokes model is employed for this problem. The solid region is represented by a single phase in the three-phase system. The rigidity constraint of the solid phase and the no-slip boundary condition on the solid-fluid interface is imposed by attributing a high viscosity to the solid phase. The solid velocity is then averaged over the solid phase region by the momentum conservation of solid phase. In the aspect of numerics, we design an efficient adaptive finite element method to solve the problem. Several numerical simulation results are given to show the capacity and efficiency of our model and numerical method.

中文翻译：

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两相流中刚性颗粒数值模拟的相场法

在本文中，我们提出了一种用于两相流中运动固体物体数值模拟的相场方法。该问题采用三相 Cahn-Hilliard 和 Navier-Stokes 模型。在三相系统中，固体区域由单相表示。固相的刚性约束和固-流界面上的无滑移边界条件是通过将高粘度赋予固相来施加的。然后通过固相的动量守恒在固相区域平均固体速度。在数值方面，我们设计了一种高效的自适应有限元方法来解决该问题。给出了几个数值模拟结果，以显示我们的模型和数值方法的能力和效率。