论文标题
用不溶性表面活性剂进行两相流的剪切有限元方法
A Cut Finite Element Method for two-phase flows with insoluble surfactants
论文作者
论文摘要
我们提出了一种新的未有限元方法，用于在存在不溶性表面活性剂的情况下模拟两相流。该方法的主要特征是1）表面活性剂质量的离散保护； 2）具有不符合不变流体的不断发展的界面的网格的可能性； 3）在不断发展的几何形状（例如速度场和压力）中，具有弱或强的不连续性的量准确近似。不可压缩的Navier的新离散化 - 稳定的方程式与对流扩散方程建模在不断发展的表面上对表面活性剂转运建模的是基于一个时空剪切有限元的公式，并在时间上具有正交和稳定项的弱配方术语，可提供功能扩展。所提出的策略利用相同的计算网格将表面部分微分方程（PDE）离散化和批量PDE，并且可以与不同的技术组合来表示和演化界面，此处使用了级别设置方法。提出了两个和三个空间维度的数值模拟，包括模拟，显示表面活性剂在两滴之间相互作用中的作用。
We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that do not conform to the evolving interface separating the immiscible fluids; 3) accurate approximation of quantities with weak or strong discontinuities across evolving geometries such as the velocity field and the pressure. The new discretization of the incompressible Navier--Stokes equations coupled to the convection-diffusion equation modeling the surfactant transport on evolving surfaces is based on a space-time cut finite element formulation with quadrature in time and a stabilization term in the weak formulation that provides function extension. The proposed strategy utilize the same computational mesh for the discretization of the surface Partial Differential Equation (PDE) and the bulk PDEs and can be combined with different techniques for representing and evolving the interface, here the level set method is used. Numerical simulations in both two and three space dimensions are presented including simulations showing the role of surfactant in the interaction between two drops.
