The origin of oscillatory convergence in finite difference methods is investigated. Fairly simple implicit schemes are used to solve the steady convection diffusion equation with variable coefficients and possible scenarios are shown that exhibit the oscillatory convergence. Also a manufactured solution to difference equations is formulated that exhibit desired oscillatory behavior in gird convergence with varying formal order of accuracy. This model-error equation is used to assess statistically the performance of several methods of extrapolation. Alternative extrapolation schemes such as the deferred extrapolation to limit technique to calculate the coefficients in the Taylor series expansion of the error function are also considered. A new method is proposed that is based on the extrapolation of approximate error and shown to be a viable alternative to the other methods. This paper elucidates the problem of oscillatory convergence and brings a new look into the problem of estimating discretization error by optimizing the information from a minimum number of calculations.
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ASME 2004 Heat Transfer/Fluids Engineering Summer Conference
July 11–15, 2004
Charlotte, North Carolina, USA
Conference Sponsors:
- Heat Transfer Division and Fluids Engineering Division
ISBN:
0-7918-4691-1
PROCEEDINGS PAPER
Limitations of Richardson Extrapolation and Possible Remedies for Estimation of Discretization Error Available to Purchase
I. B. Celik,
I. B. Celik
West Virginia University, Morgantown, WV
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C. Shaffer
C. Shaffer
West Virginia University, Morgantown, WV
Search for other works by this author on:
I. B. Celik
West Virginia University, Morgantown, WV
J. Li
West Virginia University, Morgantown, WV
G. Hu
West Virginia University, Morgantown, WV
C. Shaffer
West Virginia University, Morgantown, WV
Paper No:
HT-FED2004-56035, pp. 107-118; 12 pages
Published Online:
February 24, 2009
Citation
Celik, IB, Li, J, Hu, G, & Shaffer, C. "Limitations of Richardson Extrapolation and Possible Remedies for Estimation of Discretization Error." Proceedings of the ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. Volume 2, Parts A and B. Charlotte, North Carolina, USA. July 11–15, 2004. pp. 107-118. ASME. https://doi.org/10.1115/HT-FED2004-56035
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