Decomposition methods to solve sti propagating combustion fronts between walls onMIMD

Extended Abstract We present the special use of domain decomposition and operator splitting combined with asymp-totic analytical qualitative results to obtain, on parallel computers, more eecient and accurate solvers 4] adapted to the nature of the solution of combustion fronts. Our applications in gas combustion, solid combustion as well as frontal polymerization are characterized by stii fronts that propagate with nonlinear dynamics. The multiple scale phenomena under consideration lead to very intense computation and can be analysed formally by asymptotic methods 5, 6]. We focus our study here to combustion ame in liquid. Examples of liquid ames are given by reaction processes of frontal polymerization. Frontal polymerization is currently investigated to design new materials that cannot be produced by classical processes 15]. The interaction between a mechanism of convective instability similar to Rayleigh B enard instability and a mechanism of thermal instability well known in solid combustion 14, 8] plays a key r^ ole in such situation. Our rst step in the modelization is to couple a reaction diiusion system well known in solid combustion 14] to the Navier Stokes equations written in Boussinesq approximation. For the direct simulation, we use the Stream-Vorticity ((?!) formulation of the N-S and we consider the one step chemical reaction of the rst order. C is the concentration of the reactant and T is the temperature.