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:

$$ \begin{split} \rho\left(\frac{\partial \mathbf{u}}{\partial t} + \left(\mathbf{u}\cdot\nabla\right)\mathbf{u}\right) & = -\nabla p + \mu\left(\nabla^2\mathbf{u}+\dfrac13\nabla(\nabla\cdot\mathbf{u})\right) + \mathbf{f}, \\ \rho c_p\left(\frac{\partial T}{\partial t} + \mathbf{u}\cdot\nabla T \right) &=\nabla\cdot(k\nabla T) + q,\\ \frac{\partial Y}{\partial t} &= -Y_{\text{f}},Y,K, \\ % \nabla\cdot\mathbf{u} & = \dfrac{1}{\rho c_p T}\left(\nabla\cdot(k\nabla T) + q\right), \\ \rho (T)&=\dfrac{\rho_\infty T_{\infty}}{T}, \\ & + \text{Initial and boundary conditions}. \end{split} $$

More details in:

• San Martin, D., & Torres, C. E. (2025). Simplified coupled atmosphere‑fire model for simulation of 2D wildland fires. Computer Physics Communications. Available at: https://doi.org/10.1016/j.cpc.2025.109746

Examples

Flat terrain

Simple hill

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