Mining the discrete velocity method for high quality solutions for one-dimensional Poiseuille flow

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Abstract

A fully discretized solution for Poiseuille flow in a one-dimensional channel is presented. Unlike previous semi-analytical methods, such as the Analytical Discrete-Ordinates (ADO) or the FN methods, which have been specifically designed to avoid spatial discretization error, no analytical advantage is assumed. Instead, the solution is "mined" in a process where each discrete approximation is an element in a sequence of solutions whose convergence to the solution is accelerated. This process leads most straightforwardly to high quality benchmark results for use in algorithm verification with a minimum of theoretical and numerical complexity.

Original languageEnglish (US)
Pages (from-to)1011-1024
Number of pages14
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume57
Issue number6
DOIs
StatePublished - Nov 1 2006

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Keywords

  • Convergence acceleration
  • Discrete velocity method (DVM)
  • Poiseuille flow

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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