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Topology Optimization for Fluid Flows with Body Forces

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Topology Optimization Theory for Laminar Flow

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Abstract

This chapter presents the topology optimization method for the steady and unsteady incompressible Navier-Stokes flows driven by body forces that influence the optimal shape and topology of fluid flows.

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References

  1. R.L. Panton, Incompressible Flow (Wiley, 1984)

    Google Scholar 

  2. T. Borrvall, J. Petersson, Topology optimization of fluid in Stokes flow. Int. J. Numer. Meth. Fluids 41, 77–107 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Gersborg-Hansen, O. Sigmund, R.B. Haber, Topology optimization of channel flow problems. Struct. Multidisc. Optim. 29, 1–12 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. L.H. Olesen, F. Okkels, H. Bruus, A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow. Int. J. Numer. Meth. Eng. 65, 975–1001 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. D.N. Srinath, S. Mittal, An adjoint method for shape optimization in unsteady viscous flows. J. Comput. Phys. 229, 1994–2008 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE Constraints (Springer, 2009)

    Google Scholar 

  7. M.B. Giles, N.A. Pierce, An introduction to the adjoint approach to design. Flow, Turbul. Combust. 65, 393–415 (2000)

    Article  MATH  Google Scholar 

  8. B. Mohammadi, O. Pironneau, Applied Shape Optimization for Fluids, (Oxford, 2010)

    Google Scholar 

  9. J. Nocedal, S.J. Wright, Numerical Optimization (Springer, 1998)

    MATH  Google Scholar 

  10. K. Svanberg, The method of moving asymptotes: a new method for structural optimization. Int. J. Numer. Meth. Eng. 24, 359–373 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  11. http://www.comsol.com

  12. H. C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics, (Oxford, 2006)

    Google Scholar 

  13. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, England, 1967)

    Google Scholar 

  14. A. Gersborg-Hansen, M. Berggren, B. Dammann, Topology optimizatiopn of mass distribution problems in Stokes flow. Solid Mech. Appl. 137, 365–374 (2006)

    Google Scholar 

  15. Z. Liu, Q. Gao, P. Zhang, M. Xuan, Y. Wu, Topology optimization of fluid channels with flow rate equality constraints. Struct. Multidisc. Optim. 44, 31–37 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Osher, J.A. Sethian, Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 78, 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Zahedi, A.K. Tornberg, Delta function approximations in level set methods by distance function extension. J. Comput. Phys. 229, 2199C2219 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. B. Engquist, A.K. Tornberg, R. Tsai, Discretization of Dirac delta functions in level set methods. J. Comput. Phys. 207, 28–51 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. A.K. Tornberg, B. Engquist, Regularization techniques for numerical approximation of PDEs with singularities. J. Scientif. Comput. 19, 1–3 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. M.Y. Wang, X. Wang, D. Guo, A level set method for structural optimization. Comput. Meth. Appl. Mech. Eng. 192, 227–246 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. G. Allaire, F. Jouve, A. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363–393 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Zhou, Q. Li, A variational level set method for the topology optimization of steady-state Navier-Stokes flow. J. Comput. Phys. 227, 10178–10195 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Burger, B. Hackl, W. Ring, Incorporating topological derivatives into level set methods. J. Comput. Phys. 194, 344–362 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  24. L.H. Olessen, F. Okkels, H. Bruus, A high-level programming-language implementation of optimization applied to steady-state Navier-Stokes flow. Int. J. Numer. Meth. Eng. 65, 975–1001 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. V.J. Challis, A discrete levle-set topology optimization code written in Matlab. Struc. Multidisc. Optim. 41, 453–464 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Y. Jung, K.T. Chu, S. Torquato, A variational level set approach for surface area minimization of triply-periodic surfaces. J. Comput. Phys. 223, 711–730 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  27. P. Michaleris, D.A. Tortorelli, C.A. Vidal, Tangent operators and design sensitivity formulations for transient nonlinear coupled problems with applications to elasto-plasticity. Int. J. Numer. Meth. Eng. 37, 2471–2499 (1994)

    Article  MATH  Google Scholar 

  28. J. Nocedal, S.J. Wright, Numerical Optimization (Springer, New York, 2000)

    Google Scholar 

  29. K. Ito, K. Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications, SIAM, 2008

    Google Scholar 

  30. T. Belytschko, S.P. Xiao, C. Parimi, Topology optimization with implictly function and regularization. Int. J. Numer. Meth. Eng. 57, 1177–1196 (2003)

    Article  MATH  Google Scholar 

  31. T. Slawig, PDE-constrained control using FEMLAB-Control of the Navier-Stokes equations. Numer. Algor. 42, 107–126 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  32. H. Maatoug, Shape optimization for the Stokes equations using topological sensitivity analysis. ARIMA 5, 216–229 (2006)

    Google Scholar 

  33. S. Amstutz, The topological asymptotic for the Navier-Stokes equations. ESAIM Control Optim. Calcul. Var. 11, 401–425 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  34. S. Amstutz, Topological sensitivity analysis for some nonlinear PDE systems. J. Math. Pures Appl. 85, 540–557 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  35. G. Hauke, T.J.R. Hughes, A unified approach to compressible and incompressible flows. Comp. Meth. Appl. Mech. Eng. 113, 389–395 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  36. S. Osher, R. Fedkiw, Level set methods and dynamic implicit surfaces (Springer, New York, 2003)

    Google Scholar 

  37. C. Min, On reinitializing level set functions. J. Comput. Phys. 229, 2764–2772 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  38. J. Ducrée, S. Haeberle, S. Lutz, S. Pausch, F. Stetten, R. Zengerle, Design and fabrication of a centrifugally driven microfluidic disk for fully integrated metabolic assays on whole blood. J. Micromech. Microeng. 17, 103–115 (2007)

    Article  Google Scholar 

  39. J. Steigert, T. Brenner, M. Grumann, L. Riegger, R. Zengerle, J. Ducrée, Design and fabrication of a centrifugally driven microfluidic disk for fully integrated metabolic assays on whole blood. IEEE MEMS Conf. 229, 2764–2772 (2006)

    Google Scholar 

  40. http://scienceworld.wolfram.com/physics/Navier-StokesEquationsRotational.html

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Authors and Affiliations

  1. Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun, China

    Yongbo Deng, Yihui Wu & Zhenyu Liu

Authors
  1. Yongbo Deng
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  2. Yihui Wu
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  3. Zhenyu Liu
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Correspondence to Yongbo Deng .

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Deng, Y., Wu, Y., Liu, Z. (2018). Topology Optimization for Fluid Flows with Body Forces. In: Topology Optimization Theory for Laminar Flow. Springer, Singapore. https://doi.org/10.1007/978-981-10-4687-2_3

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  • DOI: https://doi.org/10.1007/978-981-10-4687-2_3

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4686-5

  • Online ISBN: 978-981-10-4687-2

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