Limitations of richardson extrapolation and some possible remedies

Journal of Fluids Engineering, Transactions of the ASME

Volumn 127, Issue 4, 2005, Pages 795-805

  Celik, Ismail ^a   Li, Jun ^a   Hu, Gusheng ^a   Shatter, Christian ^a  

^a West Virginia University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETIZATION ERROR; OSCILLATORY CONVERGENCE; STATISTICAL ASSESSMENT; TAYLOR SERIES;

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; ERRORS; EXTRAPOLATION; FINITE DIFFERENCE METHOD; OPTIMIZATION; PROBLEM SOLVING;

OSCILLATIONS;

EID: 24344494293     PISSN: 00982202     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1949646     Document Type: Conference Paper

References (15)

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2. Richardson, L. F., and Gaunt, J. A., 1927, "The Deferred Approach to the Limit," Philos. Trans. R. Soc. London, Ser. A 226, pp. 299-361.
3. Celik, I., Chen, C. J., Roache, P. J., and Scheurer, G., eds., 1993, "Quantification of Uncertainty in Computational Fluid Dynamics," ASME Fluids Engineering Div. Summer Meeting, 158, Washington, DC, June 20-24.
4. Roache, P. J., 1993, "A Method for Uniform Reporting of Grid Refinement Studies," Proc. of Symp. on Quantification of Uncertainty in Computational Fluid Dynamics, ASME, New York, I. Celik et al., eds., ASME Fluids Engineering Div. Summer Meeting, 158, Washington DC, June 20-24, pp. 109-120.
5. Roache, P. J., 1998, Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque.
6. Celik, I., and Zhang, W. M, 1993, "Application of Richardson Extrapolation to Some Simple Turbulent Flow Calculations," Proc. of Symp. on Quantification of Uncertainty in Computational Fluid Dynamics, ASME, New York, I. Celik et al., eds., ASME Fluids Engineering Div. Summer Meeting, 158, Washington, DC, June 20-24, pp. 29-38.
7. Celik, I., and Karatekin, O., 1997, "Numerical Experiments on Application of Richardson Extrapolation With Nonuniform Grids," ASME J. Fluids Eng. 119, pp. 584-590.
8. Stern, F., Wilson, R. V., Coleman, H. W., and Paterson, E. G., 2001, "Comprehensive Approach to Verification and Validation of CFD Simulations: Part 1. Methodology and Procedures," ASME J. Fluids Eng. 123, pp. 793-802.
9. Cadafalch, J., Perez-Segarra, C. D., Consul, R., and Oliva, A., 2002, "Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer," ASME J. Fluids Eng. 124, pp. 11-21.
10. Eca, L., and Hoekstra, M., 2002, "An Evaluation of Verification Procedures for CFD Applications," 24th Symp. on Naval Hydrodynamics, Fukuoka, Japan, July 8-13.
11. Celik, I., and Li, J., 2004, "Assessment of Numerical Uncertainty for the Calculations of Turbulent Flow over a Backward Facing Step," Workshop on Uncertainty Estimation, Lisbon, Oct. 21-22.
12. Roy, C. J., 2003, private communication.
13. Klein, M., 2004, private communication.
14. Fox, L., 1957, The Numerical Solution of Two-point Boundary Value Problems in ODE's, Clarendon Press, Oxford, pp. 332.
15. Phillips, G. M., and Taylor, P. J., 1973, Theory and Applications of Numerical Analysis, Academic Press, New York, pp. 345.