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 e lapsed time of the computation. We develop a methodology to build on t he 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 combusti on process, The first is a thermodiffusive model of a two-step chemica l reaction exhibiting two transition layers. The second is a thermo-di ffusive model of a one-step chemical reaction coupled with a hydrodyna mical model using the stream function-vorticity formulation of the Nav ier-Stokes equations written in the Boussinesq approximation. This met hodology makes use of efficient domain decomposition methods, combined with asymptotic analytical qualitative results to adapt the interface position, to solve the transition layer(s) of the solution accurately and operator splitting to take advantage of the quasi-planar property of the frontal process.Then, it provides three complementary levels o f parallelism. A first level of parallelism based on the domain decomp osition, thus a priori limited to the number of transition layers in t he problem. A second based on an explicit parallelism in the orthogona l direction of the front propagation. A third based on the spread of e quations on subnetworks of processors. The parallel implementation usi ng the message passing library concept on the Paragon and iPSC860 MIMD computers are discussed. An efficient parallel algorithm to solve the space-periodic stream-function in the second model, based on Fourier modes decomposition combined with the first and second level of parall elism is provided. The direct numerical simulation provided by our num erical method allows us to explore the physical parameter space of the combustion process in order to understand the mechanism of instabilit ies. Some examples of hydrodynamical and thermal instabilities are giv en.