Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Mathematical Modeling of Wildland-Urban Interface Fires.



Randall J. McDermott, Ronald Rehm


This paper presents a simple model to demonstrate the effect on grass-fire propagation of the winds induced by structural fires in a Wildland-Urban Interface (WUI) setting. The model combines an empirical formula for wind-driven grass-fire spread and a physics-based analytical solution to the Euler equations to determine the ground-level wind produced by the burning structure. The scaling of the wind is based on the heat release rate (HRR) of the structural fire as well as other parameters. Also considered are an ambient wind and a topographical wind, assumed to be proportional to the ground slope. Data on grass and structure fires required by the model are discussed. The model can be presented using either a Lagrangian or an Eulerian description of the fire front. Methods used to solve each description are presented and compared, with the so-called Level-Set Method (LSM) used in the latter case. The LSM has the distinct advantage that it can follow front propagation during pinching off and disappearance of a portion of the front as well as mergers with other fronts, and examples are presented of each type of behavior. Prediction of the fire front propagation in the Lagrangian description is illustrated by several examples: a front passing a single burning structure on flat terrain, a front passing a burning structure on a hill, and a front passing several burning structures. The model predicts that a fire front will be accelerated toward the burning structure upon approach and decelerated after passing the structure, thereby spending more time near the burning structure than if the structure were absent. The model also shows, as expected, that the slope of a hill will accelerate or decelerate the front, depending upon the slope magnitude and sign. Finally, several burning structures multiply the effects of an individual burning structure, causing the front to linger longer in the vicinity of the structures.
Technical Note (NIST TN) - 1712
Report Number


burning, heat release rate, model, structural fires, Wildland-Urban Interface (WUI), winds


McDermott, R. and Rehm, R. (2011), Mathematical Modeling of Wildland-Urban Interface Fires., Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 18, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created September 14, 2011, Updated June 2, 2021