Resolution of downstream boundary layers in the Chebyshev approximation to viscous flow problems

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Abstract

Steady solutions characterized by downstream boundary layers are sought to the one-dimensional linearized Burgers equation for a variety of computational-that is, spatial and temporal differencing-schemes. When well resolved, the presence of these boundary layers does not seriously affect the accuracy of the interior solutions. For narrow outflow boundary layers, however, the Chebyshev collocation method may be unstable, unlike the finite-difference technique, for grid Reynolds numbers less than a certain critical value. Although the spectral solutions are improved by using fractional step time-differencing methods in which the viscous and advective effects are separately treated, the stability of the resulting multistep technique need not be guaranteed by the stability of its component steps. Analogous computational restrictions on the use of the Chebyshev collocation method are shown to hold for the nonlinear Burgers equation.

Original languageEnglish (US)
Pages (from-to)313-324
Number of pages12
JournalJournal of Computational Physics
Volume33
Issue number3
DOIs
StatePublished - Dec 1979
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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