A continuous second-order sensitivity equation method for time-dependent incompressible laminar flows

International Journal for Numerical Methods in Fluids

Volumn 55, Issue 6, 2007, Pages 565-587

  Ilinca, Florin ^a   Pelletier, D ^b   Borggaard, J ^c  

^a NATIONAL RESEARCH COUNCIL CANADA   (Canada)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^c VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

3D finite elements; Incompressible flows; Second order sensitivity; Sensitivity equations; Time dependent flows

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; PIPE FLOW; REYNOLDS NUMBER; STROUHAL NUMBER; VORTEX FLOW; VORTEX SHEDDING;

SENSITIVITY EQUATION METHOD; UNIFORM FLOW; VON KARMAN STREET;

LAMINAR FLOW;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; LAMINAR FLOW; PIPE FLOW; REYNOLDS NUMBER; STROUHAL NUMBER; VORTEX FLOW; VORTEX SHEDDING;

EID: 35248879671     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1477     Document Type: Article

References (36)

1. Roache PJ. Verification and Validation in Computational Science and Engineering. Hermosa: Albuquerque, NM, 1998.
2. Martins JRRA, Stradza P, Alonso JJ. The complex-step derivative approximation. ACM Transactions on Mathematical Software-TOMS 2003; 29(3):245-262.
3. Putko M, Newman P, Taylor A, Green L. Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives. Fifteenth AIAA Computational Fluid Dynamics Conference, AIAA Paper 2001-2528, Anaheim, CA, June 2001.
4. Borggaard J, Burns J. A PDE sensitivity equation method for optimal aerodynamic design. Journal of Computational Physics 1997; 136(2):366-384.
5. Stanley LG, Stewart DL. Design Sensitivity Analysis: Computational Issues of Sensitivity Equation Methods. Frontiers in Applied Mathematics, vol. 25. SIAM: Philadelphia, 2001.
6. Turgeon É, Pelletier D, Borggaard J. A general continuous sensitivity equation formulation for complex flows. Numerical Heat Transfer, Part B 2002; 42:485-498.
7. Haug EJ, Choi K, Komkov V. Design Sensitivity Analysis of Structural Systems. Mathematics in Science and Engineering, vol. 17. Academic Press: Orlando, 1986.
8. Hien TD, Kleiber M. Stochastic finite element modeling in linear heat transfer. Computer methods in Applied Mechanics and Engineering 1997; 144:111-124.
9. Gunzburger MD. Perspectives in Flow Control and Optimization. SIAM: Philadelphia, 2002.
10. Sherman LL, Taylor III AC, Green L, Newman PA, Hou GW, Korivi VM. First- and second-order aerodynamic sensitivity derivatives via automatic differentiation. Journal of Computational Physics 1996; 129(2):307-331.
11. Godfrey AG, Cliff EM. Direct calculation of aerodynamic force derivatives: a sensitivity-equation approach. Thirty-sixth AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 98-0393, Reno, NV, January 1998.
12. Godfrey AG, Cliff EM. Sensitivity equations for turbulent flows. Thirty-ninth AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2001-1060, Reno, NV, January 2001.
13. Limache A. Aerodynamic modeling using computational fluid dynamics and sensitivity equations. Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2000.
14. Turgeon É, Pelletier D, Borggaard J. Computation of airfoil flow derivatives using a continuous sensitivity equation method. Eighth CASI Aerodynamics Symposium, Toronto, Canada, April 2001.
15. Blackwell BF, Dowding KJ, Cochran RJ, Dobranich D. Utilization of sensitivity coefficients to guide the design of a thermal battery. Proceedings of the 1998 ASME/IMECE, ASME, HTD-vol. 561-5, Anaheim, CA, 1998; 73-82.
16. Borggaard J, Pelletier D. Optimal shape design in forced convection using adaptive finite elements. Thirty-Sixth AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 98-0908, Reno, NV, January 1998.
17. Turgeon É, Pelletier D, Borggaard J. A general purpose sensitivity equation formulation for complex flows. Proceedings of the 8th Annual Conference of the Computational Fluid Dynamics Society of Canada, vol. 2, Montréal, Canada, 11-13 June 2000; 697-704.
18. Turgeon É, Pelletier D, Borggaard J. Applications of continuous sensitivity equations to flows with temperature-dependent properties. Numerical Heat Transfer, Part A: Applications 2003; 44:611-624.
19. Turgeon É, Pelletier D, Borggaard J. Application of a sensitivity equation method to the κ-ε model of turbulence. Fifteenth AIAA Computational Fluid Dynamics Conference, AIAA Paper 2001-2534, Anaheim, CA, June 2001.
20. Turgeon É, Pelletier D, Borggaard J. A general continuous sensitivity equation formulation for the κ-ε model of turbulence. Thirty-first AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2001-3000, Anaheim, CA, June 2001.
21. Ilinca F, Hétu J-F. Three-dimensional simulation and design sensitivity analysis of the injection molding process. NUMIFORM 2004, Columbus, OH, June 2004.
22. Turgeon É, Pelletier D, Borggaard J. A continuous sensitivity equation approach to optimal design in mixed convection. Thirty-third AIAA Thermophysics Conference, AIAA Paper 99-3625, Norfolk, VA, June-July 1999.
23. Turgeon É, Pelletier D, Borggaard J. Sensitivity and uncertainty analysis for variable property flows. Thirty-ninth AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2001-0139, Reno, NV, January 2001.
24. Hristova H, Étienne S, Pelletier D, Borggaard J. A continuous sensitivity equation method for time-dependent incompressible laminar flows. International Journal for Numerical Methods in Fluids 2006; 50:817-844.
25. Mahieu J-N, Étinne S, Pelletier D, Borggaard J. A second-order sensitivity equation method for laminar flow. International Journal of Computational Fluid Dynamics 2005; 19:143-157.
26. Hughes TJR, Franca LP, Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 1986; 59:85-99.
27. Hughes TJR, Franca LP, Hulbert GM. A new finite element formulation for computational fluid dynamics: VII. The Galerkin-least-squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering 1989; 73:173-189.
28. Franca LP, Frey SL. Stabilized finite element methods: II. The incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1992; 99(2-3):209-233.
29. Ilinca F, Hétu J-F, Pelletier D. On stabilized finite element formulations for incompressible flows. Thirteenth AIAA Computational Fluid Dynamics Conference, AIAA Paper 97-1863, Snowmass, Colorado, 1997.
30. Tezduyar TE, Shih R, Mittal S, Ray SE. Incompressible flow using stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Research Report UMSI 90/165, University of Minnesota/Supercomputer Institute, Minneapolis, 1990.
31. Tezduyar TE, Aliabadi SK, Behr M, Mittal S. Massively parallel finite element simulation of compressible and incompressible flows. Research Report 94-013, Army High Performance Computing Research Center, Minneapolis, MN, 1994.
32. Von Schwind JJ. Geophysical Fluid Dynamics for Oceanographers. Prentice-Hall: Englewood Cliffs, NJ, 1980.
33. Sohankar A, Norberg C, Davidson L. Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition. International Journal for Numerical Methods in Fluids 1998; 26:39-56.
34. Ilinca F, Pelletier D, Borggaard J. A continuous second-order sensitivity equation method for time-dependent incompressible laminar flows. Seventeenth AIAA Computational Fluid Dynamics Conference, AIAA Paper 2005-5252, Toronto, ON, 2005.
35. Williamson CHK. Defining a universal and continuous Strouhal-Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Physics of Fluids 1988; 31:2742-2744.
36. Behr M, Hastreiter D, Mittal S, Tezduyar TE. Incompressible flow past a circular cylinder; dependence of the computed field on the location of the lateral boundaries. Computer Methods in Applied Mechanics and Engineering 1995; 123:309-316.