Two-phase flows are the flows of two immiscible phases separated by an interface such as, for instance, mixtures of air and water or water and oil. They are ubiquitous in nature and central to many engineering applications, with contributions to key sectors such as energy conversion, transportation, manufacturing, and healthcare. They are also relevant for the study of climate-change and for understanding how diseases spread, e.g. through coughing and sneezing, which can be of incredibly significant public-health impact. Despite their clear importance, our understanding of the complex dynamics of two-phase flows remains limited. Computer-based simulations have played an increasingly important role in providing new insights into these complex dynamics, for instance as viable alternatives to costly experiments, but they are still limited in their scope, flexibility, efficiency, and accuracy.
This project was concerned with initiating a shift in the way two-phase flows can be accurately simulated and predicted using computing resources, leveraging the development of a new "high-order" numerical framework. Owing to its high order, the proposed numerical framework exhibits unprecedented convergence properties, i.e. an enhanced ability to produce increasingly better results as more computational resources are thrown at the problem at hand. Notably, this framework is the first of its kind ever to be able to simulate two-phase flows while both exactly conserving the mass of fluid and producing a convergent estimation of the surface-tension force distribution that acts at the interface between the two phases. This was made possible by applying one main conceptual change to the start-of-the-art, that is the replacement of planar local approximations of the interface by curved (quadratic) ones for numerically solving the governing equations of the flow. The superior performance of the newly developed framework has been demonstrated with canonical and physically realistic test-cases of two-phase flows.
