Wildfires are a problem of great interest in Chile because of the damage they cause every year to forest, wild fauna and flora, an also threatening human lives, among others. There are many computational models for numerical simulations, but very few of them are open source. The goal of this work is to build an open source framework for Chilean wildfires. In this paper, we present the numerical algorithm to be used as the core of our framework. The algorithm is based on a numerical discretization of a system of partial differential equations. The computational and mathematical components, numerical simulations and applications are described in details in the paper.