本课题主要围绕着火温度模型进行研究，分别是带有一个自由界面的着火温度模型和带有两个自由界面的着火温度模型。该模型描述的是氢-氧和乙烯-氧的混合物燃烧产生的厚火焰区中火焰传播的动力系统。研究内容包括两方面：（1）通过建模导出火焰锋方程，并建立火焰锋方程和Kuramoto-Sivashinsky方程之间的联系；（2）构造一种计算格式数值求解火焰锋方程，模拟火焰锋的动态性质，并分析计算格式的稳定性和收敛性。本项目旨在运用建模和数值模拟的方法来研究着火温度模型中的火焰传播，以此为带有自由界面的燃烧模型的研究提供新的思路和解决方法。

We consider two ignition-temperature models, one with single free interface and the other with two free interfaces. The models describe dynamics of thick flames in combustion of hydrogen-oxygen and ethylene-oxygen mixtures. This project is twofold: (1) Derive the flame front equation through modeling, then associate the front equation with Kuramoto-Sivashinsky equation. (2) Construct a numerical scheme to solve the interface and simulate the dynamic of thick flames, then analyze the stability and convergence of the proposed method. The aim of our work is to use the method of modeling and simulation to study flame propagation in ignition-temperature models, and meanwhile to provide new mathematical framework for the study of combustion models with interfaces.