Modeling the residual in error-transport equations for estimating grid-induced errors in CFD solutions

Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting

Volumn 14, Issue , 2006, Pages 10668-10676

  Qin, Y ^a   Chi, X ^b   Shih, T I P ^b  

^a CATERPILLAR INC   (United States)

^b Iowa State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE ERROR-TRANSPORT EQUATION (DETE); GRID-INDUCED ERRORS;

COMPUTATIONAL FLUID DYNAMICS; FINITE DIFFERENCE METHOD; FINITE VOLUME METHOD; NUMERICAL METHODS;

ERROR ANALYSIS;

EID: 34250783640     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (42)

1. Roache, P., Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico, 1998.
2. Oberkampf, W.L., Blottner, F.G., and Aeshliman, D., "Methodology' for Computational Fluid Dynamics Code Verification and Validation," AIAA Paper 95-2226, June 1995.
3. Cosner, R.R., Oberkampf, W.L., Rahaim, C.P., Shih, T.I-P., "AIAA Committee on Standards for Computational Fluid Dynamics - Status and Plans," AIAA Paper 2004-00654, January 2004.
4. Carey, G.F., Computational Grids: Generation, Adaptation, and Solution Strategies, Taylor & Francis, Washington, DC, 1997.
5. Celik, I., Chen, C.J., Roache, P.J., and 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.
6. Celik, I. and 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.
7. Wilson, R.V. and Stern, F., "Verification and Validation for RANS Simulation of a Naval Surface Combatant," AIAA Paper 2002-0904, Jan. 2002.
8. Peraire, J., Vahdati, M., Morgan, K., and Zienkiewicz, O.C., "Adaptive Remeshing for Compressible Flow Calculations," J. of Computational Physics, Vol. 22, 1976, pp.131-149.
9. Babuska, I. And Rheinboldt, W., "Error Estimates for Adaptive Finite Element Computations," SIAM Journal on Numerical Analysis, Vol. 15, No. 4, 1978, pp. 736-754.
10. Zienkiewicz, O.C. and 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.
11. 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.
12. 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.
13. Mackenzie, J., Sonar, T., and 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.
14. Venditti, D.A. and 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.
15. Shih, T.I-P., Gu, X., and 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.
16. Gu, X., Schock, H.J., Shih, T.I-P., Hernandez, E.C., Chu, D., Keller, P.S., and Sun, R.L., "Grid-Quality Measures for Structured and Unstructured Meshes," AIAA Paper 2001-0652, Jan. 2001.
17. Gu, X. and 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. Babuska, I., Strouboulis, T., and 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.
19. Babuska, I., Strouboulis, T., Gangaraj, S.K., and 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.
20. 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.
21. rd Annual Conference of the CFD Society of Canada, Vol. 1, Baniff, Alberta, June 1995.
22. Zhang, X.D., Trépanier, J.-Y., and 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.
23. Zhang, X.D., Pelletier, D., Trepanier, J.-Y., and Camarero, R., "Numerical Assessment of Error Estimators for Euler Equations," AIAA Journal, Vol. 39, No. 9, 2001, pp. 1706-1715.
24. Qin, Y. and Shih, T.I-P., "A Discrete Transport Equation for Error Estimation in CFD," AIAA Paper 2002-0906, January 2002.
25. Finlayson, B. A., Method of Weighted Residuals and Variational Principles, Elsevier Science & Technology Books, 1972.
26. Giles, M.B., Larson, M.G., Levenstam, J.M., and 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.
27. th ICFD Conference on Numerical Methods for Fluid Dynamics, Oxford, UK, 1998.
28. 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.
29. Giles, M.B. and Pierce, N.A., "Improved Lift and Drag Estimates Using Adjoint Euler Equations," AIAA Paper 99-3293, 1999.
30. Venditti, D.A. and Darmofal, D.L., "Anisotropic Grid Adaptation for Functional Outputs: Application to Two-Dimensional Viscous Flows," Journal of Computational Physics, Vol. 187, 2003, pp. 22-46.
31. Park, M.A., "Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation," AIAA Journal, Vol. 42, No. 9, 2004, pp. 1854-1862.
32. Qin, Y. and Shih, T.I-P., "A Method for Estimating Grid-Induced Errors in Finite-Difference and Finite-Volume Methods," AIAA Paper 2003-0845, Jan. 2003.
33. Qin, Y., Keller, P.S., Sun, R.L., Hernandez, E.C., Perng, C.Y., Trigui, N., Han, Z., Shen, F.Z., and Shih, T.I-P., "Estimating Grid-Induced Errors in CFD by Discrete-Error-Transport Equations," AIAA Paper 2004-0656, Aerospace Sciences Meeting, Reno, January 2004.
34. Qin, Y., Chi, X., and Shih, T. I-P., "Estimating Grid-Induced Errors in Navier-Stokes Solutions by Euler Discrete-Error-Transport Equations," AIAA Paper 2005-0567, Aerospace Sciences Meeting, Reno, Nevada, January 2005.
35. Warming, R. F. and 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.
36. Celik, I., Hu, G., and Badeau, A., "Further Refinement and Bench Marking of a Single-Grid Error Estimation Technique," AIAA Paper 2003-0626, Jan. 2003.
37. th Computational Fluid Dynamics Conference, Orlando, June 2003.
38. Wang, Z.J., "Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids: Basic Formulation," J. Computational Physics, Vol. 178, pp. 210-251, 2002.
39. Chi, X., Li, Y., Chen, H., Addy, H.E., Choo, Y.K., and Shih, T.I-P., "A Comparative Study Using CFD to Predict Iced Airfoil Aerodynamics," AIAA Paper 2005-1371, January 2005.
40. Mani, M., "A Structured and Hybrid- unstructured Grid Euler and Navier-Stokes Solver for General Geometry," AIAA Paper 2004-0524, Jan. 2004.
41. Nelson, C., Lankford, D., Nichols, R., "Recent Improvements to the WIND(-US) Code at AEDC," AIAA Paper 2004-0527, Jan. 2004.
42. Spalart, P.R. and Allmaras, S.R., "A One-Equation Turbulence Model for Aerodynamic Flows," AIAA Paper 1992-0439, January 1992.