A numerically accurate mathematical framework for simulations of firebrand transport in landscape-scale fire spread models

Abstract

We consider in the present study an evaluation of the numerical accuracy of the dominant approach used to model the transport of firebrands in landscape-scale fire spread simulators. The approach is based on a prescribed statistical distribution for downwind ember flight distance combined with a model for flight time. The present study assumes instantaneous ignition of spot fires following landing of firebrands on the ground, a simplification that is not realistic but one that allows performing simple verification tests for which an exact solution is available. The present study considers both a Eulerian version and a discrete particle (called Lagrangian) version of the firebrand transport model. The results of the verification tests show that the firebrand models are “numerically accurate” or “converged”, i.e., are insensitive to changes in numerical parameters provided that a set of conditions are satisfied. It is found that in the Eulerian firebrand model, numerical accuracy is controlled by the wind-based Courant-Friedrichs-Lewy (CFL) number, whereas in the Lagrangian firebrand model, numerical accuracy is controlled by both the CFL number and the generation rate of computational particles. These results provide a solid mathematical foundation for simulations of firebrand transport in landscape-scale fire spread simulators.