A Web-based Introduction to Fire Modeling
Mathematical Models
Mathematical models are what most people think of when they hear the words ?fire model?. A mathematical model is anything that, in general, is a series of equations that describe something.
The category of mathematical models can be broken down into two types, probabilistic and deterministic, with each type having its own set of equations. Deterministic models are based on the governing laws of fire dynamics. Probabilistic models rely on statistical observations and probabilistic equations.
There is no limit to what can be mathematically modeled by fire protection engineers. However, one must realize several things with mathematical models.
1. Although the sky may be the limit, modeling is a case of easier said then done.
2. Many things are still unknown about fire. Assumptions are made and these assumptions are only as good as the engineer making them. An engineer must understand the model's limitations. An engineer must validate the model with actual experimental results.
3. The equations that make a fire model come either from physical principles or from experimental data. When using experimental data the empirical equations used for the model will have the least amount of error when modeling scenarios are close to what the experiments were like.
4. We use computers only because these equations can be very long and tedious; also, sometimes a model requires many thousands of operations (or calculations). For simplification purposes all models categorized under mathematical will be assumed to also be computational. We will review these types of models in the following pages.
