Numerical Models for Two-Phase flows in Electric Fields

该项目涉及电场存在下两相流的模拟。因此，TRANSIEVES的主要目标是子项目A1中提出的实验装置的数值研究，即，乒乓状的水滴结构。第一个供资期专门用于建立模拟工具箱，并进行与A1有关的具体模拟。在第二阶段，将进一步开发这一模拟工具箱，以协助实施分离程序。这将需要比第一阶段更大的模拟，即，进一步发展以支持大规模并行高性能计算。数值模拟的物理模型是两相Navier-Stokes方程与电动力学（Poisson-Nernst-Planck）模型相结合。将使用水平设置方法跟踪流体界面。我们特别建议使用高阶，高精度的扩展间断伽辽金（XDG）方法来处理不连续的属性，如密度，粘度和介电常数。因此，XDG方法能够以高精度近似压力、粘性和麦克斯韦应力的跳跃。此外，XDG的一个变体，所谓的示踪DG方法，将被用来模拟吸附的浓度，在流体界面的离子物种。在工作计划的后面部分，将介绍马兰戈尼力，即，表面张力取决于所吸附的物质。

This project is concerned with the simulation of two-phase flows in the presence of electric fields. Thereby, its main goal within TRANSIEVES is the numerical investigation of the experimental setup proposed in subproject A1, i.e., the ping-pong droplet configuration. The first funding period is dedicated to building up the simulation toolbox and to perform specific simulations related to A1. In the second period, this simulation toolbox will be further developed to aid the implementation of separation processes. This will require larger simulations than in the first period, i.e., further development to support massive, parallel high-performance computing. The physical models underlying the numerical simulation are the two-phase Navier-Stokes equations in combination with an electrokinetic (Poisson-Nernst-Planck) model. The fluid interface will be tracked using a level-set method. We especially propose using a high-order, highly accurate extended discontinuous Galerkin (XDG) method to handle the discontinuities in properties such as density, viscosity and dielectric constant. Thereby, the XDG method is capable of approximating jumps in pressure, viscous and Maxwell stresses with a high order of accuracy. Furthermore, a variant of XDG, the so-called trace-DG method, will be used to simulate the concentration of adsorbed, ionic species at the fluid interface. In a later part of the work program, Marangoni forces will be introduced, i.e., a surface-tension that is dependent on the adsorbed species.