Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants
Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants
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DOI：
10.1016/j.jcp.2012.01.018
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
Sashikumaar Ganesan;L. Tobiska
中科院分区：
文献类型：
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作者：
Sashikumaar Ganesan;L. Tobiska
发展了一种基于任意拉格朗日-欧拉和拉格朗日耦合方法的有限元格式，用于计算可溶表面活性剂的界面流动。数值格式用于求解含时Navier-Stokes方程和体相表面活性剂浓度演化方程，同时求解界面表面活性剂浓度演化方程。用动网格上的二阶等参元和二阶等参面有限元来求解这些方程。界面解析的移动网格允许在材质参数中精确地合并表面力、Marangoni力和跳跃。用于求解表面演化方程的低维有限元网格是界面分辨运动网格的一部分。对于已知解析解的问题，数值格式得到了验证。为了研究表面活性剂对三维轴对称上升气泡的影响，进行了大量的计算。该方案具有良好的流体质量守恒性和表面活性剂总质量守恒性。
A finite-element scheme based on a coupled arbitrary Lagrangian–Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier–Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.