Numerical Experiments on Application of Richardson Extrapolation With Nonuniform Grids

Author:

Celik Ismail1,Karatekin Ozgur2

Affiliation:

1. Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV

2. Aeronautical Engineering Department, Middle East Technical University, Ankara, Turkiye

Abstract

Some unresolved problems related to Richardson extrapolation (RE) are elucidated via examples, and possible remedies are suggested. The method is applied to the case of turbulent flow past a backward facing step using nonuniform grid distributions. It is demonstrated that RE can be used to obtain grid independent solutions using the same grid refinement factors in both coordinate directions. The use of generalized wall functions together with the standard k-ε model seems to work well even if the grid refinement extends into the viscous sublayer. In addition, the grid convergence index and other standard uncertainty measures are compared, and a new uncertainty measure is suggested which seems to be a better indicator for the grid convergence error.

Publisher

ASME International

Subject

Mechanical Engineering

Reference16 articles.

1. Avva, R. K., Kline, S. J., and Ferziger, J. H., 1988, “Computation of the Turbulent Flow Over a Backward-Facing Step Using the Zonal Modeling Approach,” Stanford University, TR TF-33, Stanford CA. Also AIAA Paper 88-0611, Jan.

2. Celik, I., and Zhang, W-M., 1993 “Application of Richardson Extrapolation to Some Simple Turbulent Flow Calculations,” Proceedings of the Symposium on Quantification of Uncertainty in Computational Fluid Dynamics, I. Celik et al., eds., ASME Fluids Engineering Division Spring Meeting, Washington D. C., June 20-24, p. 29.

3. Celik I , and ZhangW-M, 1995 “Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flows Calculations,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 117, No. 3, pp. 439–445.

4. Celik, I., and Karatekin, O., 1995 “Numerical Experiments on Application of Richardson Extrapolation to a Turbulent Flow with Separation,” Proc. of the forum on “Quantification of Uncertainty in Computational Fluid Dynamics,” ASME/JSME Fluids Engineering Conference, Hilton Head, SC, Aug. 13-18.

5. Demuren A. O. , and WilsonR. V., 1994 “Estimating Uncertainty in Computations of Two-Dimensional Separated Flows,” ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 116, No. 2, pp. 216–220.

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