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People in the developed world spend the majority of their lives indoors. While inside, people can be exposed to many different gaseous and particulate contaminants. Both short term and long term exposure to these contaminants have a wide range of health related outcomes from mild discomfort to heart disease, cancer, and even death. The purpose of this research is to provide a computational framework for fast predictions of the transport of contaminants, which is used to identify optimal locations for sensors, and finally the framework is utilized to provide performance measures for ventilation system during the design stage. All these applications can be analyzed using the discrete form of the PerronFrobenius operator, also known as Markov matrices. Two different methods are developed for fast and accurate calculations of contaminant transport at large Courant numbers. Once the Markov matrices are calculated, they are used to position sensors where contaminants are likely to collect and are used to quantify mechanical ventilation performance. The methods developed may be used to develop evacuation for people during a release of a toxic gas or airborne infectious disease, execute containment plans of potentially harmful airborne contaminants, and the control of HVAC systems to provide adequate ventilation and clean/fresh air to the occupied space.

Analyzing the characteristics of contaminant transport using the Perron-Frobenius operator in indoor building environments