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.
