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

M. Garbey, D. Tromeur-Dervout

Research output: Contribution to journalArticle

14 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)316-331
Number of pages16
JournalJournal of Computational Physics
Volume145
Issue number1
DOIs
StatePublished - Sep 1 1998

Keywords

  • Chebyshev polynomials
  • Combustion
  • Domain decomposition
  • Fourier expansions
  • Parallelism

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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