Mathematical Model

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

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