Untangling the Prometheus Nightmare

A number of bush and forest fire simulators have been developed in the last two decades based on the deterministic spread equations of Gwynfor Richards (Int. J. Num. Meth. Eng. 1990) and the marker method for computing discrete approximations to the Richards equations. Unfortunately, all such implementations are plagued by topological complications. For example, sampling issues on the evolving front, represented in the Canadian simulator Prometheus as a set of polygons, lead to tangling and other non-physical singularities. Recently, an automated untangling routine has been developed for Prometheus based on the so-called 2-colour Theorem. Not only is this approach more intuitive than previous algorithms (which were based on scan lines and winding number calculations), it has proved to be more accurate and faster on all test cases employed by Prometheus developers (from 10 to 90 percent speedup compared to previous generation codes, depending on the examples). It is based on a concise and easy-to-implement set of rules which do not introduce the many ‘special cases’ that previous methods required. This report presents a brief review of fire simulation models in general, and on their various approaches to untangling in particular. We describe the mathematical foundations for our new method and give a brief overview of the programming issues that arise in implementation. Finally, we report the results obtained by the new model on a test database of fires used by Prometheus developers. Performance is assessed both in terms of run times and in the ability of the code to produce realistic fire fronts without operator intervention.