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

Author： Garbey M. Tromeur-dervout D.

Publisher： Academic Press

ISSN： 0021-9991

Source： Journal of Computational Physics, Vol.145, Iss.1, 1998-09, pp. : 316-331

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Abstract

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.