Accurate and Efficient Coupled Surfactant Calculations for Two-Phase Flows with the Discrete Exterior Calculus

在这个项目中，我们将开发一个新的，强大的，准确的和GPU并行求解器的两相流问题与表面活性剂的自由表面。基于我们现有的求解器NaSt 3DGPF，我们将应用显式网格构造方法的流体/流体界面，执行平滑的子细胞采样的推广的行军立方体算法。一个关键的功能，然后是离散外部微积分（DEC），这将被用于对界面网格的表面张力PDE的数值处理，表面张力的计算和耦合的界面PDE的体积方程具有显着不同的密度。与捕获批量离散化的尖锐界面一起，DEC承诺获得稳定性，鲁棒性和界面上的表面活性剂方程，表面张力计算和甚至接近界面的批量的更高精度。此外，我们将并行化的GPU计算节点集群的新方法，以获得一个快速的模拟工具（泰勒）气泡问题和液滴破碎在剪切驱动流中的表面活性剂的存在。

In this project, we will develop a new, robust, accurate and GPU-parallelized solver for two-phase flow problems with surfactants on the free surface. Based on our existing solver NaSt3DGPF, we will apply an explicit mesh construction method for the fluid/fluid interface which performs smooth sub-cell sampling in a generalization of the marching cubes algorithm. A key feature is then the Discrete Exterior Calculus (DEC) which will be employed on the interface mesh for the numerical treatment of the surfactant-PDE, the calculation of the surface tension and the coupling of the interface-PDE to the bulk equations with significantly different densities. Together with a sharp interface capturing bulk discretization, DEC promises to obtain stability, robustness and improved accuracy for the surfactant equations on the interface, the surface tension calculations and the bulk quantities even close to the interface. We furthermore will parallelize the new approach for a cluster of GPU compute nodes to obtain a fast simulation tool for (Taylor) bubble problems and droplet breakup in shear driven flows in the presence of surfactants.