We study the flow of a pre-mixed, reactive, incompressible, viscous fluid, using a combination of vortex methods and a flame propagation algorithm based on Huyghens' principle. The random vortex methods are lagrangian methods used to resolve the motion of incompressible fluids regulated by the Navier-Stokes equations. They are best suited for flows at high Reynolds numbers. Detailed description of the vortex blobs, and vortex sheets methods is given together with the presentation of a hybrid vortex method that relates the two. The combustion part of the problem is modeled by a variation of the SLIC (Simple Line Interface Calculation) algorithm, that involves the use of a flame dictionary which contains flame speeds and preheat thicknesses. The combined algorithms are tested on a cold flat late with different free stream velocities. The numerical results show the effects of cold boundaries, turbulence, and exothermicity on the burning process
