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 a new parallel direct solver of 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 the nonperiodic case 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. (C) 1998 Academic Press.