Construction of solution curves for large two-dimensional problems of steady-state flows of incompressible fluids

V. F. De Almeida, J. J. Derby

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

This work represents a step toward advancing classical methods of bifurcation analysis in conjunction with very large-scale scientific computing needed to model realistically processes which involve laminar and steady flows of incompressible fluids. A robust method of analysis based on pseudoarclength continuation, Newton's method, and direct solution of linear systems is proposed and applied to the analysis of a representative system of fluid mechanics, namely the tilted lid driven cavity. Accurate solution curves, possessing simple singular points, were computed for Reynolds numbers varying from 0 to 10,000 and for different angles of tilt. The results demonstrate that two-dimensional models with up to 1,000,000 algebraic equations can be studied feasibly using the methods described here with state-of-the-art vector supercomputers.

Original languageEnglish (US)
Pages (from-to)285-311
Number of pages27
JournalSIAM Journal on Scientific Computing
Volume22
Issue number1
DOIs
StatePublished - Dec 1 2000

Keywords

  • Factorization of large unsymmetric sparse matrices
  • Incompressible and viscous fluids
  • Lid driven cavity
  • Navier-Stokes equations
  • Parameter continuation
  • Path following

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