Topology optimization of slightly compressible fluids

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 86, Issue 1, 2006, Pages 46-62

  Evgrafov, Anton ^a  

^a University of Colorado   (United States)

Author keywords

Domain identification; Fictitious domain; Fluid mechanics; Navier Stokes flow; Topology optimization

Indexed keywords

EID: 31344456460     PISSN: 00442267     EISSN: None     Source Type: Journal    
DOI: 10.1002/zamm.200410223     Document Type: Article

References (60)

1. L. Ambrosio, N. Fusco, and D. Pallara, Functions of Bounded Variation and free Discontinuity Problems, Oxford Mathematical Monographs (The Clarendon Press Oxford University Press, New York, 2000).
2. G. Allaire, Arch. Ration. Mech. Anal. 113(3), 209-259 (1990).
3. G. Allaire, Arch. Ration. Mech. Anal. 113(3), 261-298 (1990).
4. J.-P. Aubin and H. Frankowska, Set-Valued Analysis (Birkhäuser Boston Inc., Boston, MA, 1990).
5. F. Beux and A. Dervieux, Finite Eiern. Anal. Des. 12(3-4), 281-302 (1992).
6. J. C. Bellido, Existence of Classical Solutions for a One-Dimensional Optimal Design Problem in Wave Propagation, Preprint (2003), Mathematical Institute, University of Oxford, Oxford, UK. Submitted for publication.
7. M. P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods, and Applications (Springer-Verlag, Berlin, 2003).
8. J. A. Bello, E. Fernández Cara, and J. Simon, Optimal shape design for Navier-Stokes flow, in: System Modelling and Optimization (Zurich, 1991), Lecture Notes in Control and Inform. Sci., Vol. 180 (Springer, Berlin, 1992), pp. 481-489.
9. J. Borggaard and J. Burns, A sensitivity equation approach to shape optimization in fluid flows, in: Flow Control (Minneapolis, MN, 1992), IMA Vol. Math. Appl., Vol. 68 (Springer, New York, 1995), pp. 49-78.
10. B. Bourdin and A. Chambolle, ESAIM, Control, Optimisation Calc. Var. 9, 19-48 (2003).
11. T. Borrvall and J. Petersson, Comput. Methods Appl. Mech. Eng. (Elsevier) 190(37-38), 4911-4928 (2001).
12. T. Borrvall and J. Petersson, Int. J. Numer. Methods Fluids 41(1), 77-107 (2003).
13. T. Borrvall, Arch. Comput. Methods Eng. 8(4), 351-385 (2001).
14. J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems (Springer-Verlag, New York, 2000).
15. B. Bourdin, Int. J. Numer. Methods Eng. 50(9), 2143-2158 (2001).
16. H. Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications [Theory and Applications] (Masson, Paris, 1983).
17. T.E. Bruns and D. A. Tortorelli, Comput. Methods Appl. Mech. Eng. (Elsevier) 190(26-27), 3443-3459 (2001).
18. G. F. Carey and R. Krishnan, Comput. Methods Appl. Mech. Eng. (Elsevier) 42(2), 183-224 (1984).
19. A. Chakib and T. Ghemires, Math-Rech. Appl. 4, 47-64 (2002).
20. O. Darrigol, Arch. Hist. Exact Sci. 56(2), 95-150 (2002).
21. Q. V. Dinh, G. Rogé, C. Sevin, and B. Stoufflet, Rev. Eur. Elem. Finis 5(5-6), 569-594 (1996).
22. R. Dziri and J.-P. Zolésio, J. Convex Anal. 6(2), 293-318 (1999).
23. I. Ekeland and R. Témam, Convex Analysis and Variational Problems, Classics in Applied Mathematics, Vol. 28, English ed., translated from the French (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999).
24. A. Evgrafov, The Limits of Porous Materials in the Topology Optimization of Stokes Flows, Applied Mathematics and Optimization (Springer-Verlag, New York), DOI 10.1007/s00245-005-0828-z.
25. E. Feireisl, Appl. Math. Optim. 47(1), 59-78 (2003).
26. P. Fernandes, J.M. Guedes, and H. Rodrigues, Comput. Struct. 73(6), 583-594 (1999).
27. M. Fuchs and G. Seregin, Variational methods for problems from plasticity theory and for generalized Newtonian fluids, Lecture Notes in Mathematics, Vol. 1749 (Springer-Verlag, Berlin, 2000).
28. G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I, Springer Tracts in Natural Philosophy, Linearized steady problems, Vol. 38 (Springer-Verlag, New York, 1994).
29. A. Gersborg-Hansen, Topology Optimization of Incompressible Newtonian Flows at Moderate Reinolds Numbers, Master's thesis, Department of Mechanical Engineering, Technical University of Denmark, December 2003.
30. M.D. Gunzburger, Hongchul Kim, and S. Manservisi, Math. Model. Numer. Anal. 34(6), 1233-1258 (2000).
31. A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics (Springer-Verlag, New York, 2003).
32. M. D. Gunzburger and Hongchul Kim, SIAM J. Control Optim. 36(3), 895-909 (1998).
33. M. Gunzburger and S. Manservisi, Flow matching by shape design for the Navier-Stokes system, in: Optimal Control of Complex Structures (Oberwolfach, 2000), Int. Ser. Numer. Math., Vol. 139 (Birkhäuser, Basel, 2002), pp. 279-289.
34. M.D. Gunzburger, Finite Element Methods for Viscous Incompressible Flows, Computer Science and Scientific Computing (Academic Press Inc., Boston, MA, 1989).
35. M.D. Gunzburger, Perspectives in Flow Control and Optimization, Advances in Design and Control (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003).
36. R. B. Haber, M.P. Bendsøe, and C.S. Jog, Perimeter constrained topology optimization of continuum structures, in: IUTAM Symposium on Optimization of Mechanical Systems (Stuttgart, 1995), Solid Mech. Appl., Vol.43 (Kluwer Acad. Publ., Dordrecht, 1996), pp. 113-120.
37. J.C. Heinrich and C.A. Vionnet, Arch. Comput. Methods Eng. 2(2), 51-65 (1995).
38. U. Hornung (ed.), Homogenization and Porous Media, Interdisciplinary Applied Mathematics, Vol. 6 (Springer-Verlag, New York, 1997).
39. H. Kim, J. Korean Math. Soc. 38(1), 1-23 (2001).
40. A. Klarbring, J. Petersson, B. Torstenfeit, and M. Karlsson, Comput. Methods Appl. Mech. Eng. (Elsevier) 192(35-36), 3909-3932 (2003).
41. A. Kufher, Weighted Sobolev Spaces, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], with German, French and Russian summaries, Vol. 31 (BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1980).
42. S.Y. Lin, Y. S. Chin, and T. M. Wu, SIAM J. Sci. Comput. 16(1), 1-19 (1995).
43. B. Mohammadi and O. Pironneau, Applied Shape Optimization for Fluids, Numerical Mathematics and Scientific Computation (Oxford University Press, New York, 2001).
44. P. Neittaanmäki, V. Rivkind, and G. Serëgin, Optirn. Control Appl. Methods 16(2), 143-148 (1995).
45. H. Okumura and M. Kawahara, Comput. Model. Eng. Sci. 1(2), 71-77 (2000).
46. J. Petersson and O. Sigmund, Int. J. Numer. Methods Eng. 41(8), 1417-1434 (1998).
47. J. Petersson, Comput. Methods Appl. Mech. Eng. (Elsevier) 171(1-2), 123-140 (1999).
48. O. Pironneau, J. Fluid Mech. 59, 117-128 (1973).
49. O. Pironneau, J. Fluid Mech. 64, 97-110 (1974).
50. R.T. Rockafellar and R. J.-B. Wets, Variational Analysis (Springer-Verlag, Berlin, 1998).
51. O. Sigmund, Mech. Struct. Mach. 25(4), 493-524 (1997).
52. O. Sigmund and J. Petersson, Struct. Multidiscip. Optim. 16(1), 68-75 (1998).
53. J. Soko lowski, and Jean-Paul Zolésio, Introduction to Shape Optimization, Springer Series in Computational Mathematics, Vol. 16 (Springer-Verlag, Berlin, 1992).
54. S. Stojanovic and T.P. Svobodny, A variational approach to shape optimization for the Navier-Stokes equations, in: Optimal Control of Differential Equations (Athens, OH, 1993), Lecture Notes in Pure and Appl. Math., Vol. 160 (Dekker, New York, 1994), pp. 281-291.
55. A. P. Suetov, A shape optimization algorithm for the minimum drag problem in Stokes flow, in: Modelling and Optimization of Distributed Parameter Systems (Warsaw, 1995) (Chapman and Hall, New York, 1996), pp. 375-383.
56. R. Temam, Navier-Stokes Equations, Reprint of the 1984 edition (AMS Chelsea Publishing, Providence, RI, 2001).
57. B. A. Ton, J. Optim. Theory Appl. 118(1), 135-156 (2003).
58. B. A. Ton, SIAM J. Control Optim. 41(6), 1733-1747 (2003).
59. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Mathematical Library, Vol. 18 (North-Holland Publishing Co., Amsterdam, 1978).
60. E.H. van Brummelen and A. Segal, Int. J. Numer. Methods Fluids 40(3-4), 605-614 (2002), ICFD Conference on Numerical Methods for Fluid Dynamics, Part II (Oxford, 2001).