TITLE:
The Mathematical Model of Short-Term Forest Fire Spread
AUTHORS:
Sunben Chiu, Ying Li, Jiayi Zhao
KEYWORDS:
Forest Fire Spread Model, Spatial Velocity Field, Eikonal Equation, Dynamic Simulation, Non-Uniform Rational B-Spline
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
31,
2022
ABSTRACT: In this paper, we establish a mathematical model of the forest fire spread process based on a partial differential equation. We describe the distribution of time field and velocity field in the whole two-dimensional space by vector field theory. And we obtain a continuous algorithm to predict the dynamic behavior of forest fire spread in a short time. We use the algorithm to interpolate the fire boundary by cubic non-uniform rational B-spline closed curve. The fire boundary curve at any time can be simulated by solving the Eikonal equation. The model is tested in theory and in practice. The results show that the model has good accuracy and stability, and it’s compatible with most of the existing models, such as the elliptic model and the cellular automata model.