An Efficient Spectral-Projection Method for the Navier-Stokes Equations in Cylindrical Geometries: I. Axisymmetric Cases

J. M. Lopez, Jie Shen

Research output: Contribution to journalArticle

87 Scopus citations

Abstract

An efficient and accurate numerical scheme is presented for the axisymmetric Navier-Stokes equations in primitive variables in a cylinder. The scheme is based on a new spectral-Galerkin approximation for the space variables and a second-order projection scheme for the time variable. The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition. A sensible comparison is made with a standard second-order (in time and space) finite difference scheme based on a stream function-vorticity formulation and with available experimental data. The numerical results indicate that both schemes produce very reliable results and that despite the singular boundary condition, the spectral-projection scheme is still more accurate (in terms of a fixed number of unknowns) and more efficient (in terms of CPU time required for resolving the flow at a fixed Reynolds number to within a prescribed accuracy) than the finite difference scheme. More importantly, the spectral-projection scheme can be readily extended to three-dimensional nonaxisymmetric cases.

Original languageEnglish (US)
Pages (from-to)308-326
Number of pages19
JournalJournal of Computational Physics
Volume139
Issue number2
DOIs
StatePublished - Jan 20 1998
Externally publishedYes

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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