The first part of this thesis deals with detonations in gaseous reactive mixtures. Various technological applications have been proposed involving detonations, particularly in the field of propulsion. However, it has been confirmed experimentally that detonations generally exhibit an unstable behaviour, leading to complicated flow structures. A thorough understanding of the evolution of detonation waves is needed before they can be used for propulsion purposes. Herein, we present the first detailed numerical study of three-dimensional structures in gaseous detonations. This study is based on a parallelized, unsplit, shock-capturing algorithm. We show that we can reproduce all types of detonations that have been observed experimentally. The advancements in the field of gaseous compressible reactive flows paved the way for the study of the significantly more complex phenomena that occur in the flow of two-phase, heterogeneous compressible reactive mixtures. In the second part of this thesis, we develop a new shock-capturing algorithm for the study of these flows. We first present a new numerical procedure for solving exactly the Riemann problem of compressible two-phase flow models containing non-conservative products. We then examine the accuracy and robustness of three known methods for the integration of the non-conservative products. The issue of existence and uniqueness of solutions to the Riemann problem is also discussed. Due to the ill-posedness of the Riemann problem of standard two-phase models, we present and analyze, in the third and last part of this work, a conservative approximation to reduced one-pressure one-velocity models for compressible two-phase flows that contain non-conservative products. Herein, we develop an exact Riemann solver for the proposed reduced model. Further, we investigate the structure of the steady two-phase detonation waves admitted by this model. Finally, we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures. The effect of the solid particles on the structure of the resulting two-phase detonation is discussed in detail.

In recent years, natural, man-made and technological disasters have been increasing in magnitude and frequency of occurrence. Terrorist attacks have increased after the September 11, 2001. Some authorities suggest that global warming is partly the blame for the increase in frequency of natural disasters, such as the series of hurricanes in the early-2000's. Furthermore, there has been noticeable growth in population within many metropolitan areas not only in the US but also worldwide. These and other facts motivate the need for better emergency evacuation route planning (EERP) approaches in order to minimize the loss of human lives and property. This research considers aspects of evacuation routing never before considered in research and, more importantly, in practice. Previous EERP models only either consider unidirectional evacuee flow from the source of a hazard to destinations of safety or unidirectional emergency first responder flow to the hazard source. However, in real-life emergency situations, these heterogeneous, incompatible flows occur simultaneously over a bi-directional capacitated lane-based travel network, especially in unanticipated emergencies. By incompatible, it is meant that the two different flows cannot occupy a given lane and merge or crossing point in the travel network at the same time. In addition, in large-scale evacuations, travel lane normal flow directions can be reversed dynamically to their contraflow directions depending upon the degree of the emergency. These characteristics provide the basis for this investigation. This research considers the multiple flow EERP problem where the network travel lanes can be reconfigured using contraflow lane reversals. The first flow is vehicular flow of evacuees from the source of a hazard to destinations of safety, and the second flow is the emergency first responders to the hazard source. After presenting a review of the work related to the multiple flow EERP problem, mathematical formulations are proposed for three variations of the EERP problem where the objective for each problem is to identify an evacuation plan (i.e., a flow schedule and network contraflow lane configuration) that minimizes network clearance time. Before the proposed formulations, the evacuation problem that considers only the flow of evacuees out of the network, which is viewed as a maximum flow problem, is formulated as an integer linear program. Then, the first proposed model formulation, which addresses the problem that considers the flow of evacuees under contraflow conditions, is presented. Next, the proposed formulation is expanded to consider the flow of evacuees and responders through the network but under normal flow conditions. Lastly, the two-flow problem of evacuees and responders under contraflow conditions is formulated. Using real-world population and travel network data, the EERP problems are each solved to optimality; however, the time required to solve the problems increases exponentially as the problem grows in size and complexity. Due to the intractable nature of the problems as the size of the network increases, a genetic-based heuristic solution procedure that generates evacuation network configurations of reasonable quality is proposed. The proposed heuristic solution approach generates evacuation plans in the order of minutes, which is desirable in emergency situations and needed to allow for immediate evacuation routing plan dissemination and implementation in the targeted areas.

Previous research on ECN and RED usually considered only a limited traffic domain, focusing on networks with a small number of homogeneous flows. The behavior of RED and ECN congestion control mechanisms in TCP network with many competing heterogeneous flows in the bottleneck link, hasn't been sufficiently explored. This thesis first investigates the behavior and performance of RED with ECN congestion control mechanisms with many heterogeneous TCP Reno flows using the network simulation tool, ns-2. By comparing the simulated performance of RED and ECN routers, this study finds that ECN does provide better goodput and fairness than RED for heterogeneous flows. However, when the demand is held constant, the number of flows generating the demand has a negative effect on performance. Meanwhile, the simulations with many flows demonstrate that the bottleneck router's marking probability must be aggressively increased to provide good ECN performance. Based on these simulation results, an Adaptive ECN algorithm (AECN) was studied to further improve the goodput and fairness of ECN. AECN divides all flows competing for a bottleneck into three flow groups, and deploys a different max for each flow group. Meanwhile, AECN also adjusts min for the robust flow group and max to get higher performance when the number of flows grows large. Furthermore, AECN uses mark-front strategy, instead of mark-tail strategy in standard ECN. A series of AECN simulations were run in ns-2. The simulations show clearly that AECN treats each flow fairer than ECN with the two fairness measurements: Jain's fairness index and visual max-min fairness. AECN has fewer packet drops and alleviates the lockout phenomenon and yields higher goodput than ECN.