A stabilized finite element method for shape optimization in low Reynolds number flows

International Journal for Numerical Methods in Fluids

Volumn 54, Issue 12, 2007, Pages 1451-1471

  Srinath, D N ^a   Mittal, S ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Adjoint methods; Finite elements; Fluid flow; Multiple solutions; Shape optimization

Indexed keywords

DESIGN; DRAG COEFFICIENT; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; REYNOLDS NUMBER; SHAPE OPTIMIZATION;

ADJOINT METHODS; MULTI-OBJECTIVE FUNCTION; MULTIPLE SOLUTIONS;

FLOW OF FLUIDS;

DESIGN; DRAG COEFFICIENT; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FLOW OF FLUIDS; REYNOLDS NUMBER; SHAPE OPTIMIZATION;

EID: 34548168617     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1432     Document Type: Article

References (34)

1. Nocedal J, Wright SJ. Numerical Optimization. Springer Series in Operations Research. Springer: New York, 1999.
2. Squire W, Trapp G. Using complex variables to estimate derivatives of real functions. SIAM Review 1998; 40(1):110-112.
3. Newman III JC, Whitefield DL, Anderson WK. A step-size independent approach for multidisciplinary sensitivity analysis. Journal of Aircraft 2003; 40(3):566-573.
4. Burg COE, Newman III JC. Computationally efficient, numerical exact design derivatives via the complex Taylor's series expansion method. Computers and Fluids 2003; 32:373-383.
5. Martins JPRA, Kroo IM, Alonso JJ. An automated method for sensitivity analysis using complex variables. AIAA Paper 000-0689, 2000.
6. Newman JC III, Taylor AC III, Barnwell RC, Newman PA, Hou GJW. Overview of sensitivity analysis and shape optimization for complex aerodynamic configurations. Journal of Aircraft 1999; 36(1):87-96.
7. Hou GJW, Maroju V, Taylor III VC, Korivi M, Newman PA. Transonic turbulent airfoil design optimization using automatic differentiation in incremental iterative form. AIAA Paper 1995-1692.
8. Sherman LL, Taylor III AC, Green LL, Newman PA, Hou GJW, Korivi M. First and second order aerodynamic sensitivity derivatives via automatic differentiation with incremental iterative methods. Journal of Computational Physics 1994; 129:307-331.
9. Hou GJW, Sheen JS, Chuang CH. Shape sensitivity analysis and design optimization of linear thermoclastic solids. AIAA Journal 1992; 30(2):528-537.
10. Giles MB, Pierce NA. An introduction to the adjoint approach to design. Flow, Turbulence and Combustion 2000; 65:393-415.
11. Gunzburger MD. Sensitivities, adjoints and flow optimization. International Journal for Numerical Methods in Fluids 1999; 31:53-78.
12. Pironneau O. On optimum profiles in Stokes flow. Journal of Fluid Mechanics 1973; 59:117-128.
13. Pironneau O. On optimum design in fluid mechanics. Journal of Fluid Mechanics 1974; 64:97-110.
14. Jameson A. Aerodynamic design via control theory. Journal on Scientific Computing 1988; 59:117-128.
15. Abraham FV. Stabilized finite element solution of optimal control problems in computational fluid dynamics. Ph.D. Dissertation, Mechanical Engineering and Materials Science, Rice University, 2004.
16. Nadarajah S, Jameson A. Studies of the continuous and discrete adjoint approaches to automatic aerodynamic optimization. AIAA Paper 2000-0667, 2000.
17. Reuthers J, Jameson A, Farmer J, Martinelli L, Saunders D. Aerodynamic shape optimization of complex aircraft configurations via adjoint formulations. AIAA Paper 96-0094, 1996.
18. Kyle Anderson W, Venkarakrishnan V. Aerodynamic design optimization on unstructured grids with a continuous adjoint formulations. AIAA Paper 97-0643, 1997.
19. Brezillion J, Gauger NR. 2D and 3D aerodynamic shape optimization using the adjoint approach. Aerospace Science and Technology 2004; 8:715-727.
20. Kim S, Alonso JJ, Jameson A. Two-dimensional high lift aerodynamic optimization using the continuous adjoint method. AIAA Paper 2000-4741, 2000.
21. Soto O, Lohner R, Yang C. An adjoint-based design methodology for CFD problems. International Journal of Numerical Methods for Heat and Fluid Flow 2004; 14:734-759.
22. Soto O, Lohner R. CFD shape optimization using an incomplete-gradient adjoint formulation. International Journal for Numerical Methods in Engineering 2001; 51:735-753.
23. Elliot J, Perraire J. Practical three-dimensional design and optimization using unstructures meshes. AIAA Journal 1997; 35:1479-1485.
24. Anderson W, Bonhaus D. Airfoil design on unstructured grids for turbulent flows. NASA TM 112867, 1997.
25. Gunzburger Md. Adjoint equation-based methods for control problems in incompressible, viscous flows. Flow, Turbulence and Combustion 2000; 65:249-272.
26. Mohammadi B, Pirroneau O. Shape optimization in fluid mechanics. Annual Review of Fluid Mechanics 2004; 36:255-279.
27. Abraham F, Behr M, Heinkenschloss M. Shape optimization in steady blood flow: a numerical study of non-Newtonian effects. Computer Methods in Biomechanics and Biomedical Engineering 2005; 8:127-137.
28. Abraham F, Behr M, Heinkenschloss M. Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects. Computer Methods in Biomechanics and Biomedical Engineering 2005; 8:201-212.
29. Yagi H, Kawahara M. Shape optimization of a body located in low Reynolds number flow. International Journal for Numerical Methods in Fluids 2005; 48:819-833.
30. Okumura H, Kawahara M. Shape optimization of a body located in incompressible Navier-Stokes flow based on optimal control theory. Computer Modelling in Engineering and Sciences 2000; 1:71-77.
31. Tezduyar TE, Mittal S, Ray SE, Shih R. Incompressible flow computations with stabilized bilinear and linear equal order interpolation velocity pressure elements. Computer Methods in Applied Mechanics and Engineering 1992; 95:221-242.
32. Byrd RH, Lu P, Nocedal J, Zhu C. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing 1995; 16:1190-1208.
33. Farin G. Curves and Surfaces for Computer Aided Geometric Design. A Practical Guide. Academic Press: New York, 1990.
34. Tezduyar TE, Behr M, Mittal S, Johnson AA. Computation of unsteady incompressible flows with the finite element methods - space-time formulations, iterative strategies and massively parallel implementations. In New Methods in Transient Analysis, Smolinski P, Liu WK, Hulbert G, Tamma K (eds). AMD-vol. 143. ASME: New York, 1992; 7-24.