Projection methods can be used to enforce a divergence constraint on a velocity field. Our aim is to find a velocity field satisfying a divergence constraint with a source term represented by a Dirac delta function along a front. The projection involves the resolution of a Poisson equation with a singularity on the right hand side term over an irregular domain. A description of the Cartesian grid embedded boundary method and of the regularization of the singularity source for solving this equation will be given. An application of this method is a forest fire model that includes the feedback of the heat release at the front on the local wind.