The built environment is responsible for about 30\% of greenhouse gas emissions in the US. The design of green buildings that use significantly less energy, especially for cooling, requires mathematical models that can assist architects and designers to create new designs. I will discuss one aspect - the use of natural ventilation in buildings which are cooled by using the thermal energy they acquire either through solar heating or from gains within the building from people and equipment. This kind of analysis was used to optimize the design of the new San Diego Children's Museum, among others.