A New Parallel Solver for the Nonperiodic Incompressible Navier-Stokes Equations with a Fourier Method: Application to Frontal Polymerization

We present a specific use of domain decomposition and decomposition in function space combined with asymptotic analytical qualitative results to obtain, on parallel computers, efficient and accurate solvers [3] for rapidly varying quasi-planar unsteady combustion fronts in liquids. In particular, we give anew parallel direct solverof the unsteady incompressible Navier-Stokes equations in the stream function formulation. This solver is based on an embedding technique that allows us to generalize our previous results from the case with periodic boundary conditions [6, 7] to thenonperiodiccase with wall boundary conditions in a direction perpendicular to front propagation. The solution is decomposed into a particular solution, suitable for a Fourier method, and the general homogeneous solution, calculated from an analytic solution with high precision, to satisfy the boundary conditions. The algorithm is implemented for parallel computers and results in a very effective code. Results on the effect of the convection onto the front propagation are provided.