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

数学模型和计算机模拟为研究自然界和技术应用中所见的复杂流体流动模式提供了强大的工具。这项提案的重点是火焰、森林火灾、爆炸和水滴。更好地了解这些现象最终将有助于设计更高效的发动机，更好地管理森林和火灾风险，设计更安全的方法来处理潜在的爆炸性过程，并提出在非常小的范围内操纵流体混合物的新方法。这些问题都是棘手的研究问题。首先，数学模型是困难的、非线性的、多维的偏微分方程组，其解是不明确的，并且可能表现出严重的非线性和不连续性。其次，所有这些现象都有两个共同的特征，每个特征都构成了一个具有挑战性的研究课题：流动本质上是多尺度的--流动的小细节对全球行为有重要影响--流动表现出尖锐的锋面，例如火焰锋面或液滴内部流体与周围空气之间的界面。新颖的建模策略，结合最先进的数值方法、高性能计算机和来自详细实验的反馈，为尝试解决这些问题开辟了新的途径。

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.