Massively parallel computation of stiff propagating combustion fronts

Gas combustion, solid combustion as well as frontal polymerization are characterized by stiff fronts that propagate with nonlinear dynamics. The multiple-scale phenomena under consideration lead to very intense computations that require parallel computing in order to reduce the elapsed time of the computation. We develop a methodology to build on the MIMD architecture a parallel numerical method based on the property of the solution, i.e. a stiff quasi-planar two-dimensional combustion front. We illustrate our methodology using two models of the combustion process. The first is a thermo-diffusive model of a two-step chemical reaction exhibiting two transition layers. The second is a thermo-diffusive model of a one-step chemical reaction coupled with a hydrodynamical model using the stream function - vorticity formulation of the Navier - Stokes equations written in the Boussinesq approximation. This methodology makes use of efficient domain decomposition methods, combined with asymptotic analytical qualita...