Multiscale simulations of reactive and non-reactive fluid flows with interfaces

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Mathematical models and computer simulations provide powerful tools to investigate the complex fluid flow patterns seen in nature and in technological applications. This proposal focuses on flames, forest fires, explosions, and droplets. A better understanding of those phenomena will ultimately help design more efficient engines, better manage forests and fire risks, design safer ways of dealing with potentially explosive processes, and suggest novel ways of manipulating fluid mixtures at very small scales. Those problems are difficult research questions. First, the mathematical models are difficult, non-linear, multi-dimensional, partial differential equations, whose solutions are not known explicitly, and can exhibit severe nonlinearities and discontinuities. Second, all those phenomena have in common two features that each constitute a challenging research topic: the flows are intrinsically multiscale - the small details of the flows have an important influence on the global behavior - and the flows exhibit sharp fronts, such as the flame front or the interface between the fluid inside the droplet and the air surrounding it. Novel modeling strategies, combined with state-of-the-art numerical methods, high performance computers and feedback from detailed experimentations open new avenues to try to tackle those questions.