Mathematical Sciences: Instabilities and Pattern Formation in Flames

本课题研究了非均匀流场和密闭环境下火焰的传播问题。研究者将推导和分析适当的数学模型，并将研究这种结构下火焰的动力学。所采用的方法是将渐近摄动技术与数值计算相结合。主要目标是构建解决方案，允许对这些过程中涉及的相关物理机制有一个基本的理解，并能够与实验观察进行定性比较。密闭容器内的燃烧是一个常见的问题，但人们对它还没有很好的了解。该项目的结果将更好地描述所涉及的物理问题，并可用于验证密闭燃烧的数值模拟。

The project is concerned with problems of flame propagation in nonuniform flow fields and in confined environments. The investigator will derive and analyze appropriate mathematical models and will study the dynamics of flames in such configurations. The methods to be used are asymptotic and perturbation techniques combined with numerical computations. The primary goal is to construct solutions that permit a fundamental understanding of the relevant physical mechanisms involved in these processes and to enable qualitative comparison with experimental observations. Combustion in closed vessels is a commonly encountered problem, but it is not well understood. The results of this project will provide a better picture of the physics involved and can be used to validate numerical simulations of confined combustion.