Collaborative Research: "An Adaptive hp-Finite Element Method for Two-Fluid Flows with Topological Change"

研究人员提出了一种方法，用于执行具有拓扑变化的多流体流动问题的高分辨率模拟。该方法结合了网格变形自适应算法和hp有限元法，以获得较高的空间精度。通过使用网格细化准则来检测即将到来的拓扑变化并自动细化网格，从而提供多尺度分辨率。为了允许拓扑更改（流体界面的重新连接），在拓扑更改事件周围的小空间和时间窗口中使用水平集公式。拓扑改变完成后，移除窗口，继续进行高精度变形网格模拟。该方法将为具有拓扑变化的多流体问题提供比以前更高的精度和效率。所开发的技术也可以用于诸如拓扑变化窗口的分子动力学等公式，因此它们是迈向拓扑变化实际问题的第一性原理预测的一步。具有拓扑变化的流动的例子包括波浪撞击、空化、气泡流动、沸腾、雾化、模具填充、气体中的液体射流、涂层流动等。许多实用装置的设计取决于对这些流动的准确预测。一个这样的例子是液体燃料喷射到喷气发动机或内燃机。这些装置的性能在很大程度上取决于喷油器的性能。（大多数人都熟悉清洁汽车燃油喷射器以提高效率和减少污染物产生的想法）。目前的喷射器设计几乎完全采用试错法，因为目前的分析和数值工具无法预测过程。本研究旨在开发一种模拟技术，为具有拓扑变化的实际流提供准确可靠的预测。

The investigators propose a methodology for performing highly resolved simulations of multi-fluid flow problems with topological change. The methodology combines a mesh deformation and adaptation algorithm and an hp-finite element method to obtain high spatial accuracy. Multi-scale resolution is provided by using a mesh refinement criterion that detects oncoming topological change and automatically refines the mesh. To allow topology change (reconnection of fluid interfaces), a level-set formulation is used in a small spatial and temporal window around the topology change event. Once the topology change is complete, the window is removed and the high-accuracy deforming mesh simulation is continued. This approach will provide better accuracy and efficiency than previously possible for multi-fluid problems with topological change. The techniques developed can also be used with formulations such as molecular dynamics for the topological change window and thus they are the step towards a first-principles prediction of practical problems with topological change.Examples of flows having topological change include wave crashing, cavitation, bubbly flows, boiling, atomization, mold-filling, liquid jets in a gas, coating flows, etc. The design of many practical devices hinges on an accurate prediction of these flows. One such example is liquid fuel injection into either jet engines or internal combustion engines. The performance of these devices is strongly dependent on the performance of the fuel injectors. (Most people are familiar with the idea of getting their automobile fuel injectors cleaned to increase efficiency and reduce pollutant production). Injectors are currently designed almost entirely using a trial and error approach because current analytical and numerical tools cannot predict the process. This investigation aims to develop a simulation technique that will provide accurate and reliable predictions of practical flows having topological change.