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TECHNICAL PAPERS

Code Verification by the Method of Manufactured Solutions

[+] Author and Article Information
Patrick J. Roache

Consultant, P.O. Box 3379, Los Lunas, NM 87031e-mail: hermosa@swcp.com

J. Fluids Eng 124(1), 4-10 (Nov 12, 2001) (7 pages) doi:10.1115/1.1436090 History: Received July 24, 2001; Revised November 12, 2001
Copyright © 2002 by ASME
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References

Roache, P. J., 1998, Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, NM.
Roache, P. J., 1999, Fundamentals of Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM, Chapter 18.
Roache,  P. J., Ghia,  K., and White,  F., 1986, “Editorial Policy Statement on the Control of Numerical Accuracy,” ASME J. Fluids Eng., 108, No. 1, Mar., p. 2.
Steinberg,  S., and Roache,  P. J., 1985, “Symbolic Manipulation and Computational Fluid Dynamics,” J. Comput. Phys., 57, No. 2, Jan., pp. 251–284.
Oberkampf, W. L., Blottner, F. G., and Aeschliman, D. P., 1995, “Methodology for Computational Fluid Dynamics Code Verification/Validation,” AIAA Paper 95-2226, 26th AIAA Fluid Dynamics Conference, 19–22 June, San Diego, California.
Oberkampf, W. L., and Trucano, T. G., 2000, “Validation Methodology in Computational Fluid Dynamics,” AIAA Paper 2000–2549, 19–22 June, Denver, CO.
Oberkampf, W. L., and Trucano, T. G., 2002, “Verification and Validation in Computational Fluid Dynamics,” AIAA Progress in Aerospace Sciences (to appear).
Pelletier, D., and Ignat, L., 1995, “On the Accuracy of the Grid Convergence Index and the Zhu-Zienkiewicz Error Estimator,” pp. 31–36 in ASME FED Vol. 213, Quantification of Uncertainty in Computational Fluid Dynamics, Aug., R. W. Johnson and E. D. Hughes, eds.
Reed,  H. L., Haynes,  T. S., and Saric,  W. S., 1998, “CFD Validation Issues in Transition Modeling,” AIAA J., 36, No. 5, May, pp. 742–749. See also AIAA Paper 96-2051, 27th AIAA Fluid Dynamics Conference, 17–20 June 1996, New Orleans, Louisiana.
Polya, G., 1957, How to Solve It; A New Aspect of Mathematical Method, Princeton University Press, Princeton, NJ.
Dee, D. P., 1991, “Prescribed Solution Forcing Method for Model Verification in Hydraulic Engineering,” Proc. 1991 National Conference on Hydraulic Engineering, ASCE, Nashville, July 29-August 2.
Ethier,  C. R., and Steinman,  D. A., 1994, “Exact Fully 3D Navier-Stokes Solutions for Benchmarking,” Int. J. Fract., 19, pp. 369–375.
Powers,  J. M., and Gonthier,  K. A., 1992, “Reaction Zone Structure for Strong, Weak Overdriven and Weak Underdriven Oblique Detonations,” Phys. Fluids A, 4, No. 9, Sept., pp. 2082–2089.
Powers,  J. M., and Stewart,  D. S., 1992, “Approximate Solutions for Oblique Detonations in the Hypersonic Limit,” AIAA J., 30, No. 3, Mar., pp. 726–736.
Grismer,  M. J., and Powers,  J. M., 1992, “Comparison of Numerical Oblique Detonation Solutions with an Asymptotic Benchmark,” AIAA J., 30, No. 12, Dec., pp. 2985–2987.
Grismer,  M. J., and Powers,  J. M., 1996, “Numerical Predictions of Oblique Detonation Stability Boundaries,” Shock Waves, 6, pp. 147–156.
Salari, K., and Knupp, P., 2000, “Code Verification by the Method of Manufactured Solutions,” SAND2000-1444, Sandia National Laboratories, Albuquerque, NM 87185, June.
Salari, K., and Roache, P. J., 1990, “The Influence of Sweep on Dynamic Stall Produced by a Rapidly Pitching Wing,” AIAA Paper 90-0581.
Roache, P. J., and Steinberg, S., 1985, “A New Approach to Grid Generation Using a Variational Formulation,” AIAA 85-1527-CP, Proceedings AIAA 7th Computational Fluid Dynamics Conference, 15–17 July, Cincinnati, Ohio.
Steinberg,  S., and Roache,  P. J., 1986, “Using MACSYMA to Write Fortran Subroutines,” Journal of Symbolic Computation, 2, pp. 213–216. See also MACSYMA Newsletter, Vol. II-2, 1985, pp. 10–12.
Steinberg,  S., and Roache,  P. J., 1986, “Variational Grid Generation,” Numerical Methods for Partial Differential Equations, 2, pp. 71–96.
Steinberg, S., and Roache, P. J., 1986, “A Tool Kit of Symbolic Manipulation Programs for Variational Grid Generation,” AIAA Paper No. 86-0241, AIAA 24th Aerospace Sciences Meeting, 6–9 January 1986, Reno, Nevada.
Steinberg, S., and Roache, P. J., 1986, “Grid Generation: A Variational and Symbolic-Computation Approach,” Proceedings Numerical Grid Generation in Fluid Dynamics Conference, July, Landshut, W. Germany.
Steinberg,  S., and Roache,  P. J., 1992, “Variational Curve and Surface Grid Generation,” J. Comput. Phys., 100, No. 1, pp. 163–178.
Roy, C. J., McWherter-Payne, M. A., and Oberkampf, W. L., 2000, “Verification and Validation for Laminar Hypersonic Flowfields,” AIAA 2000-2550, June, Denver.
Roy, C. J., 2001, “Grid Convergence Error Analysis for Mixed-Order Numerical Schemes,” AIAA Paper 2001–2606, June, Anaheim. See also this issue of ASME JFE.
Pautz, S. D., 2001, “Verification of Transport Codes by the Method of Manufactured Solutions: the ATTILA Experience,” Proc. ANS International Meeting on Mathematical Methods for Nuclear Applications, M&C 2001, Salt Lake City, Utah, Sept.
AIAA, 1998, “Guide for the Verification and Validation of Computational Fluid Dynamics Simulations,” American Institute of Aeronautics and Astronautics, AIAA-G-077-1998, Reston, VA.

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