Numerical modelling and simulation of complex multiphase flows.

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Multiphase flows are ubiquitous in Nature and Technology so that it is estimated that over half of industrial applications involve to some extent multiphase flow processes. Engineers face unprecedented challenges because of the increasing complexity of the analyses needed to design multiphase flow systems. This research focuses on separated flows (as opposed to dispersed flows) and rely on computational models to improve the predictive capability and scientific analysis of multiphase flow systems. While direct numerical simulations is more and more used, there are many difficulties that are not currently addressed by available commercial software though the strategic importance of such tools. Hence, we target the development of a adaptive finite-element front capturing methodology along with an implicit fully-coupled solution procedure with highly stable time integrators. The proposed simulation approach will lead to higher fidelity models incorporating complex physics. Furthermore, anisotropic adaptivity will guarantee error levels in solutions so that reliable multiphase flow analysis can be performed with a high degree of confidence. Hence it will pave the way to the scientific analysis of multiphase flow phenomena and allow for simulations that are beyond the reach of existing solvers. A second aspect is to provide engineers with low-cost surrogate models of multiphase flow systems to speed up the design cycle of products. Indeed, the simulation methodology just described leads to computationally demanding models that produce solutions with a level of details mandatory for scientific understanding but which usually far exceeds what is needed to design engineering systems. We propose to use reduced-order modelling to reduce the mathematical complexity of these large numerical models to yield low-cost approximations required for performing the numerous repeated analyses essential in design optimization.