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来执行高分辨率的模拟拓扑变化的多流体流动问题。 该方法结合了网格变形和自适应算法和HP有限元法，以获得高的空间精度。 多尺度分辨率是通过使用网格细化准则，检测即将到来的拓扑变化，并自动细化网格。 为了允许拓扑变化（流体界面的重新连接），在拓扑变化事件周围的小空间和时间窗口中使用水平集公式。 拓扑更改完成后，将删除窗口，并继续进行高精度变形网格模拟。 这种方法将提供更好的精度和效率比以前可能的拓扑变化的多流体问题。 所开发的技术也可以与诸如拓扑变化窗口的分子动力学的公式一起使用，因此它们是朝向具有拓扑变化的实际问题的第一原理预测的步骤。具有拓扑变化的流的示例包括波碰撞、空化、气泡流、沸腾、雾化、模具填充、气体中的液体射流、涂层流、许多实际装置的设计都取决于对这些流动的准确预测。 一个这样的例子是将液体燃料喷射到喷气发动机或内燃发动机中。 这些装置的性能在很大程度上取决于喷油器的性能。 (Most人们熟悉清洁汽车燃料喷射器以提高效率和减少污染物产生的想法）。 喷射器目前几乎完全使用试错法设计，因为当前的分析和数值工具无法预测该过程。 本研究的目的是开发一种模拟技术，将提供准确和可靠的预测具有拓扑变化的实际流动。

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.