In this project the principal investigator will employ analytical and numerical methods to study the behavior of solutions of the system of partial differential equations that describes combustion phenomena in a reactive multi-phase flow. In particular, he will look at the following three inter-related problems for reactive multi-phase flows: the transition to detonation, the structure of detonation waves, and the modelling of phenomena at low Mach number,i.e., subsonic flow. A substantial part of the project involves replacing the complex set of equations with simpler, asymptotic versions whose solutions still retain the essential physics of the phenomena. The goal is to increase our understanding of the complex physics that governs the formation and evolution of flames in combustible granular flows. Combustion phenomena form a visible and important part of everyday life. Understanding the complex physical and chemical processes that occur when liquids and gases burn is therefore of interest to a host of scientists and engineers. Much of the work on combustion phenomena today is experimental and/or numerical, but the complexity of the problems often defeats even the largest supercomputer. And experiments at high temperatures are often too difficult or too expensive to perform. In this project the principal investigator will use asymptotic methods to simplify the complicated set of nonlinear equations that governs combustion in gases. He will then analyze this simpler set of equations in order to develop a better understanding of the propagation of flames in a granular flow.
