Linear Fourier and iteration-delay analysis of a computational fluid dynamics problem during execution

Joseph John Cor, Timothy Francis Miller, Joel D. Richter

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The basic equations for the Fourier error analysis are developed and then applied to the scalar conservation equation of a sample computational fluid dynamics (CFD) problem in which variables are continuously updated. The analysis helps explain basic features of numerical stability. When divergence and neutral stability are encountered, Fourier analysis provides insight into the emergence and location of the instability, but is not by itself found to be a sufficient indicator of the existence of numerical instability. Further analysis of central differencing cases is made using a variation on time-delay reconstruction, from chaos theory.

Original languageEnglish (US)
Pages (from-to)387-407
Number of pages21
JournalNumerical Heat Transfer, Part B: Fundamentals
Volume52
Issue number5
DOIs
StatePublished - Nov 1 2007

Fingerprint

Convergence of numerical methods
Fourier Analysis
Dynamic Problem
computational fluid dynamics
Computational Fluid Dynamics
iteration
Computational fluid dynamics
Iteration
Chaos Theory
Numerical Instability
Fourier analysis
Numerical Stability
Error Analysis
Chaos theory
Error analysis
Conservation
Time Delay
Time delay
Divergence
numerical stability

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications

Cite this

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Linear Fourier and iteration-delay analysis of a computational fluid dynamics problem during execution. / Cor, Joseph John; Miller, Timothy Francis; Richter, Joel D.

In: Numerical Heat Transfer, Part B: Fundamentals, Vol. 52, No. 5, 01.11.2007, p. 387-407.

Research output: Contribution to journalArticle

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