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.

Issue Section:
Research Papers
Topics:
Errors, Turbulence, Uncertainty
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
Zhang
W-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
Wilson
R. V.
,
1994
“
Estimating Uncertainty in Computations of Two-Dimensional Separated Flows
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
116
, No.
2
, pp.
216
–
220
.
6.
Karniadakis, G., Yakhot A., Rakip, S., Orzag, S. A., and Yakhot, V., 1989 “Spectral Element-RNG Simulations of Turbulent Flows in Complex Geometries,” Proceedings of 7th Symposium on Turbulent Shear Flows, Paper 7.2, Stanford University Press.
7.
Kim
J.
,
Kline
S. J.
, and
Johnston
J. P.
,
1980
“
Investigation of Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
102
, p.
302
302
.
8.
Launder
B. E.
and
Spalding
D. B.
,
1974
, “
The Numerical Computation of Turbulent Flow
,”
Computational Methods in Applied Mechanics and Engineering
, Vol.
3
, pp.
269
–
289
.
9.
Ludwig, J. C., Qin, H. Q., and Spalding, D. B., 1989, The PHOENICS Reference Manual, CHAM TR/200, CHAM Limited, Bakery House, 40 High Str., Wimbledon Village, London SW195AU, England.
10.
Richardson
L. F.
,
1910
, “
The Approximate Arithmetic Solution by Finite Differences of Physical Problems Involving Differential Equations, with Application to Stresses in a Masonry Dam
,”
Transactions of the Royal Society of London, Series A.
, Vol.
210
, pp.
307
–
357
.
11.
Roache
P. J.
,
1994
, “
Perspective: A Method for Uniform Reporting of Grid Refinement Studies
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
116
, pp.
405
–
413
.
12.
Roache, P. J., 1996, Private Communication
13.
Rosten, H. I. and Worrell, J. K., 1988, “Generalized Wall Functions for Turbulent Flow,” Cham Ltd., Bakery House, High Street, Wimbledon, London SW19 5AU, England.
14.
Speziale
C. G.
and
Thangam
S.
,
1992
, “
Analysis of an RNG Based Turbulence Model for Separated Flows
,”
International Journal of Engineering Science
, Vol.
30
, No.
10
, pp.
1379
–
1388
.
15.
Thangam
S.
and
Speziale
C. G.
,
1992
, “
Turbulent Flow Past a Backward Facing Step: A Critical Evaluation of Two-Equation Models
,”
AIAA Journal
, Vol.
30
, No.
5
, pp.
1314
–
1320
.
16.
Thangam
S.
and
Hur
N.
,
1991
, “
A Highly Resolved Numerical Study of Turbulent Separated Flow Past a Backward-Facing Step
,”
International Journal of Engineering Science
, Vol.
29
, No.
5
, pp.
607
–
615
.
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