Topology optimization of fluid domains: Kinetic theory approach

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 88, Issue 2, 2008, Pages 129-141

  Evgrafov, Anton ^a   Fingen, Georg ^a   Maute, Kurt ^a  

^a University of Colorado at Boulder   (United States)

Author keywords

Bhatnagar Gross Krook kinetic model; Domain identification; Fictitious domain; Fluid mechanics; Immersed boundary technique; Navier stokes flow; Porous materials; Topology optimization

Indexed keywords

EID: 39449134595     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200700122     Document Type: Article

References (59)

1. G. Allaire, Arch. Rational Mech. Anal. 113(3), 209-259 (1990).
2. G. Allaire, Shape optimization by the homogenization method, Applied Mathematical Sciences, Vol. 146 (Springer-Verlag, New York, 2002).
3. G. Allaire, F. Jouve, and A. M. Toader, C. R. Math. Acad. Sci. Paris 334(12), 1125-1130 (2002).
4. G. Allaire, F. Jouve, and A. M. Toader, J. Comput. Phys. 194(1), 363-393 (2004).
5. P. Angot, C. H. Bruneau, and P. Fabrie, Numer. Math. 81(4), 497-520 (1999).
6. L. Arkeiyd, On stationary kinetic systems of Boltzmann type and their fluid limits, in: Nonlocal elliptic and parabolic problems, Banach Center Publ., Vol. 66 (Polish Acad. Sci., Warsaw, 2004), pp. 13-27.
7. L. Arkeryd and A. Nouri, Ann. Fac. Sci. Toulouse Math. (6) 9(3), 375-413 (2000).
8. L. Arkeryd and A. Nouri, Ark. Mat. 43(1), 29-50 (2005).
9. M. P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods, and Applications (Springer-Verlag, Berlin, 2003).
10. M. P. Bendsøe and N. Kikuchi, Comput. Methods Appl. Mech. Engrg. 71(2), 197-224 (1988).
11. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94(3), 511-525 (1954).
12. J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems (Springer-Verlag, New York, 2000).
13. T. Borrvall and J. Petersson, Internat. J. Numer. Methods Fluids 41(1), 77-107 (2003).
14. H. C. Brinkmann, Appl. Sci. Res., Sect. A 1, 27 (1947).
15. C. Cercignani, Mathematical methods in kinetic theory (Plenum Press, New York, 1969).
16. C. Cercignani, Rarefied gas dynamics: From basic concepts to actual calculations, Cambridge Texts in Applied Mathematics (Cambridge University Press, Cambridge, 2000).
17. S. Chapman and T. G. Cowling, The mathematical theory of nonuniform gases, 2 edition (Cambridge University Press, London, 1952).
18. P. Charrier and B. Dubroca, C. R. Math. Acad. Sci. Paris 336(6), 537-542 (2003).
19. L. de Socio, N. Ianiro, and L. Marino, Mathematical Models and Methods in Appl. Sciences 11, 1273-1283 (2001).
20. L. Dumas and F. Golse, SIAM J. Appl. Math. 60(4), 1447-1470 (electronic) (2000).
21. A. Evgrafov, G. Fingen, and K. Maute, Topology optimization of fluid problems by the lattice Boltzmann method, in: IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials: Status and Perspectives, edited by M. P. Bendsøe, N. Olhoff, and O. Sigmund (Springer: Netherlands, 2006), pp. 559-568.
22. A. Evgrafov, Appl. Math. Optim. 52(3), 263-267 (2005).
23. A. Evgrafov, ZAMM Z. Angew. Math. Mech. 86(1), 46-62 (2005).
24. M. C. Geier, Z. Liu, A. Greiner, and J. G. Korvink, Lattice Boltzmann based structural topology optimization of micro channels, Submitted to J. Fluid. Mech., 2006.
25. A. Geoffrion, Interfaces 7(1), 81-92 (1976).
26. A. Gersborg-Hansen, M. P. Bendsøe, and O. Sigmund, Topology optimization using the finite volume method, in: Proceedings of WCSMO6, (2005).
27. A. Gersborg-Hansen, O. Sigmund, and R. Haber, Struct, and Multidisc. Optim. 30 (3), 181-192 (2005).
28. A. Gersborg-Hansen, Topology optimization of incompressible Newtonian flows at moderate Remolds numbers, Master's thesis, Department of Mechanical Engineering, Technical University of Denmark, December 2003.
29. J. Guest and J. Prévost, Int. J. Solids Struct. 43 (22-23), 7028-7047 (2006).
30. J. Guest and J. Prévost, International Journal for Numerical Methods in Engineering 66, 461-484 (2006).
31. M. D. Gunzburger, Perspectives in flow control and optimization, Advances in Design and Control (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003).
32. M. D. Gunzburger and H. Kim, SIAM J. Control Optim. 36(3), 895-909 (1998).
33. A. Heintz, Boundary value problems for nonlinear Boltzmann equation in domains with irregular boundaries, PhD thesis, Leningrad State University, 1986.
34. E. E. Höök, Topologioptimeringens tillämpningar inom fluidmekaniken: En förstudie, Tech. Rep. LiTH-IKP-Ex-1981, Department of Mechanical Engineering, Linköping University, 2003.
35. S. Kaplan and J. Davis, Nucl. Sci. Eng. 28, 166-176 (1967).
36. F. R. Klimetzek, J. Paterson, and O. Moos, Autoduct: topology optimization for fluid flow, in: Proceedings of Konferenz für angewandte Optimierung, Karlsruhe, (2006).
37. N. Kogan, Appl. Math. Mech. 22, 597-607 (1958).
38. G. I. Marchuk and V. I. Agoshkov, SIAM J. Numer. Anal. 18(2), 242-261 (1981).
39. N. B. Maslova, Nonlinear evolution equations: Kinetic approach, Series on Advances in Mathematics for Applied Sciences, Vol. 10 (World Scientific Publishing Co. Inc., River Edge, NJ, 1993).
40. N. Masmoudi, ESAIM Control Optim. Calc. Var. 8, 885-906 (electronic) (2002), A tribute to J. L. Lions.
41. E. A. Mason and A. P. Malinauskas, Gas Transport in Porous Media: The Dusty-Gas Model, Chemical Engineering Monographs (Elsevier Science, 1983).
42. B. Mohammadi and O. Pironneau, Applied shape optimization for fluids, Numerical Mathematics and Scientific Computation (Oxford University Press, New York, 2001).
43. O. Moos, F. R. Klimetzek, and R. Rossmann, Bionic optimization of air-guiding systems, in: Proceedings of SAE 2004 World Congress & Exhibition, Detroit, MI, USA, (Society of Automotive Engineering, Inc, 2004), pp. 95-100.
44. C. Moyne and M. Murad, Transp. Porous Media 50(1-2), 127-151 (2003), Physicochemical and electromechanical interactions.
45. F. Murat, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5(3), 489-507 (1978).
46. F. Okkels and H. Bruus, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 75(1), 016301 (2007).
47. G. Fingen, A. Evgrafov, and K. Maute, Struct. Multidiscip. Optim. 34(6), 507-524 (2007).
48. A. S. Piquemal, G. Chiavassa, and R. Donat, A Brinkman-penalization method for compressible viscous flows, submitted to Computers and Fluids, July 2004.
49. O. Pironneau, J. Fluid Mech. 59, 117-128 (1973).
50. O. Pironneau, J. Fluid Mech. 64, 97-110 (1974).
51. L. Saint-Raymond, Ann. Sci. École Norm. Sup. (4) 36(2), 271-317 (2003).
52. Y. Sone, Kinetic theory and fluid dynamics, Modeling and Simulation in Science, Engineering and Technology (Birkhäuser Boston Inc., Boston, MA, 2002).
53. M. A. A. Spaid and J. Frederick R. Phelan, Physics of Fluids 9(9), 2468-2474 (1997).
54. L. Tartar, Compensated compactness and applications to partial differential equations, in: Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV,, Res. Notes in Math., Vol. 39 (Pitman, Boston, Mass., 1979), pp. 136-212.
55. M. Thellner, Multi-parameter topology optimization in continuum mechanics, PhD thesis, Division of Mechanics, Department of Mechanical Engineering, Linköpings University, 2005.
56. V. S. Vladimirov, Trudy Mat. Inst. Steklov. 61, 158 (1961).
57. S. W. Vong, J. Differential Equations 222(1), 95-136 (2006).
58. P. Welander, Arkiv Fysik 7, 507-553 (1954).
59. N. Wiker, A. Klarbring, and T. Borrvall, Internat. J. Numer. Methods Engrg. 69(7), 1374-1404 (2006).