dsanmartin/wildfire

Coupled Atmosphere-Wildfire Model Implementation

Coupled Atmosphere-Wildfire Model

Numerical implementation of a simplified coupled atmosphere-fire mathematical model.

Mathematical model

This code solves the following system of PDEs to simulate the spread of wildfires:

$$ \begin{split} \nabla\cdot\mathbf{u} &= 0 \\ \dfrac{\partial \mathbf{u}}{\partial t} + \left(\mathbf{u}\cdot\nabla\right)\mathbf{u} &= -\dfrac{1}{\rho}\nabla p + \nu\nabla^2\mathbf{u} + \mathbf{f}(\mathbf{u}, T) \\ \dfrac{\partial T}{\partial t} + \mathbf{u}\cdot\nabla T &= k\nabla^2T + S(T, Y) \\ \dfrac{\partial Y}{\partial t} &= -Y_{\text{f}}YK(T) \\ & + \text{Initial and boundary conditions}. \end{split} $$

More details in:

• Simplified coupled atmosphere-fire model for simulation of 2D wildland fires by Daniel San Martin & Claudio E. Torres. Preprint available at: https://dx.doi.org/10.2139/ssrn.4673376

Examples

Flat terrain

Simple hill