Estimating grid-induced errors in CFD solutions

Frontiers of Computational Fluid Dynamics 2006

Volumn , Issue , 2005, Pages 183-198

  Shih, T I P ^a  

^a Iowa State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967430750     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812703187_0009     Document Type: Chapter

References (36)

1. Addy, H.E., "Ice Accretions and Icing Effects for Modem Airfoils," NASAlTP 2000-21003 1, April 2000.
2. Babuska, I. & Rheinboldt, W., "Error Estimates for Adaptive Finite Element Computations," SIAM Journal on Numerical Analysis, Vol. 15, NO. 4, 1978, pp. 736-754.
3. Babuska, I., Strouboulis, T., & Upadhyay, C.S., "A Model Study of the Quality of a Posteriori Error Estimator for Linear Elliptic Problems: Error Estimation in the Interior of Patchwise Uniform Grid of Triangles," Computer Methods in Applied Mechanics and Engineering, Vol. 114, 1994, pp. 307-378.
4. Babuska, I., Strouboulis, T., Gangaraj, S.K., & Upadhyay, C.S., "Pollution Error in the h-Version of the Finite Element Method and Local Quality of the Recovered Derivatives," Computer Methods in Applied Mechanics and Engineering, Vol. 140, 1997, pp. 1-37.
5. Carey, G.F., Computational Grids: Generation, Adaptation, and Solution Strategies, Taylor & Francis, Washington, DC, 1997.
6. Celik, I., Chen, C.J., Roache, P.J., & Scheuer, G., Editors, Symposium on Quantification of Uncertainty in Computational Fluid Dynamics, FED-Vol. 158, ASME Fluids Engineering Division, Summer Meeting, Washington D.C., 1993.
7. Celik, I. & Zhang, W.-M., "Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flow Calculations," ASME Journal of Fluids Engineering, Vol. 117, September 1995, pp. 439-445.
8. Celik, I., Hu, G., & Badeau, A., "Further Refinement and Bench Marking of a Single-Grid Error Estimation Technique," AIAA Paper 2003-0626, Jan. 2003.
9. Chi, X., Zhu, B., Shih, T.1-P., Addy, H.E., & Choo, Y.K., "CFD Analysis of the Aerodynamics of a Business-Jet Airfoil with Leading-Edge Ice Accretion," AIAA Paper 2004-0560, January 2004.
10. Ferziger, J.H., "Estimation and Reduction of Numerical Error," in Symposium on Quantification of Uncertainty in Computational Fluid Dynamics, FED-Vol. 158, ASME Fluids Engineering Division, Summer Meeting, Washington D.C., 1993, pp. 1-8.
11. Finlayson, B. A., Method of Weighted Residuals and Variational Principles, Elsevier Science & Technology Books, 1972.
12. Giles, M.B., Larson, M.G., Levenstam, J.M., & Suli, E., "Adaptive Error Control for Finite Element Approximations of the Lift and Drag Coefficients in Viscous Flow," Report NA-97/06, Oxford University Computing Laboratory, 1997.
13. Giles, M.B. & Pierce, N.A., "On the Properties of Solutions of the Adjoint Euler Equations," 6th ICFD Conference on Numerical Methods for Fluid Dynamics, Oxford, UK, 1998.
14. Giles, M.B., "On Adjoint Equations for Error Analysis and Optimal Grid Adaptation," in Frontiers of Computational Fluid Dynamics, D.A. Caughey and M.M. Hafez editors, World Scientific, 1998, pp. 155-170.
15. Giles, M.B. & Pierce, N.A., "Improved Lift and Drag Estimates Using Adjoint Euler Equations," AIAA Paper 99-3293, 1999.
16. Gu, X., Schock, H.J., Shih, T.1-P., Hernandez, E.C., Chu, D., Keller, P.S., & Sun, R.L., "Grid-Quality Measures for Structured and Unstructured Meshes," AIAA Paper 2001-0652, Jan. 2001.
17. Gu, X. & Shih, T.I-P., "Differentiating between Error Source and Error Location in Solution-Adaptive Mesh Refinement," AIAA Paper 2001 -2660, CFD Conference, June 2001.
18. Mackenzie, J., Sonar, T., & Suli, E., "Adaptive Finite Volume Methods for Hyperbolic Problems," Mathematics of Finite Elements and Applications, edited by J.R. Whiteman, John Wiley and Sons, New York, 1994, Chapter 19.
19. Oden, J.T., "Error Estimation and Control in Computational Fluid Dynamics," Mathematics of Finite Elements and Applications, edited by J.R. Whiteman, John Wiley and Sons, New York, 1994, Chapter 1.
20. Peraire, J., Vahdati, M., Morgan, K., & Zienkiewicz, O.C., "Adaptive Remeshing for Compressible Flow Calculations," J. of Computational Physics, Vol. 22, 1976, pp.131-149.
21. Qin, Y. & Shih, T.I-P., "A Discrete Transport Equation for Error Estimation in CFD," AIAA Paper 2002-0906, January 2002.
22. Qin, Y. & Shih, T.I-P., "A Method for Estimating Grid-Induced Errors in Finite-Difference and Finite-Volume Methods," AIAA Paper 2003-0845, Jan. 2003.
23. Qin, Y. Shih, T.I-P., "Analysis and Modeling of the Residual in the Discrete Error Transport Equation," AIAA Paper 2003-3850, June 2003.
24. Qin, Y., Keller, P.S., Sun, R.L., Hernandez, E.C., Perng, C.Y., Trigui, N., Han, Z., Shen, F.Z., & Shih, T.I-P., "Estimating Grid-Induced Errors in CFD by Discrete-Error-Transport Equations," AIAA Paper 2004-0656, January 2004.
25. Qin, Y., Chi, X., & Shih, T. I-P., "Estimating Grid-Induced Errors in Navier-Stokes Solutions by Euler Discrete-Error-Transport Equations," AIAA Paper 2005-0567, January 2005.
26. Roache, P., Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico, 1998.
27. Shih, T.I-P., Gu, X., & Chu, D., "Grid-Quality Measures and Error Estimates," in Numerical Grid Generation in Computational Field Simulations, B.K. Soni, J.F. Thompson, J. Hauser, and P.R. Eiseman, editor, Mississippi State University, ISSG, 2000, pp. 799-808.
28. Sonar, T., "Strong and Weak Norm Refinement Indicators Based on the Finite Element Residual for Compressible Flow Computations," Impact of Computing in Science and Engineering, Vol. 5, 1993, pp. 111-127.
29. van Straalen, B.P., Simpson, R.B., & Stubley, G.D., "A Posteriori Error Estimation for Finite-Volume Simulations of Fluid Flow Transport," Proceedings of the 3rd Annual Conference of the CFD Society of Canada, Vol. 1, Baniff, Alberta, June 1995.
30. Venditti, D.A. & Darmofal, D.L., "Adjoint Error Estimation and Grid Adaptation for Functional Outputs: Application to Quasi-One-Dimensional Flow," Journal of Computational Physics, Vol. 164,2000, pp. 204-227.
31. Wang, Z.J., "Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids: Basic Formulation," J. Computational Physics, Vol. 178, pp. 210-251,2002.
32. Warming, R. F. & Hyett, B. J., "The Modified Equation Approach to the Stability and Accuracy Analysis of Finite-difference Methods," J. Comp. Physics, Vol. 14, 1974, pp. 159-179.
33. Wilson, R.V. & Stem, F., "Verification and Validation for RANS Simulation of a Naval Surface Combatant," AIAA Paper 2002-0904, Jan. 2002.
34. Zhang, X.D., Trkpanier, J.-Y., & Camarero, R., "A Posteriori Error Estimation for Finite-Volume Solutions of Hyperbolic Conservation Laws," Computational Methods in Applied Mechanics and Engineering, Vol. 185, 2000, pp. 1-19.
35. Zhang, X.D., Pelletier, D., Trkpanier, J.-Y., & Camarero, R., "Numerical Assessment of Error Estimators for Euler Equations," AIM Journal, Vol. 39, NO. 9,2001, pp. 1706-1715.
36. Zienkiewicz, O.C. & Zhu, J.Z., "A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis," International J. for Numerical Methods in Engineering, Vol. 24, 1987, pp. 337-357.