Skip to main content
SpringerLink
Log in

Adjoint shape optimization for fluid–structure interaction of ducted flows

  • Review Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

Based on the coupled problem of time-dependent fluid–structure interaction, equations for an appropriate adjoint problem are derived by the consequent use of the formal Lagrange calculus. Solutions of both primal and adjoint equations are computed in a partitioned fashion and enable the formulation of a surface sensitivity. This sensitivity is used in the context of a steepest descent algorithm for the computation of the required gradient of an appropriate cost functional. The efficiency of the developed optimization approach is demonstrated by minimization of the pressure drop in a simple two-dimensional channel flow and in a three-dimensional ducted flow surrounded by a thin-walled structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Farhat C, van der Zee K, Geuzaine P (2006) Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput Methods Appl Mech Eng 195:1973–2001

    Article  MathSciNet  MATH  Google Scholar 

  2. Willcox K, Paduano J, Peraire J (1999) Low order aerodynamic models for aeroelastic control of turbomachines. In: Proceedings of 40thAIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials(SDM) Conference St. Louis, USA, pp 1–11

  3. Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412

    Article  MATH  Google Scholar 

  4. Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143

    Article  MATH  Google Scholar 

  5. Jameson A (1995) Optimum aerodynamic design using CFD and control theory. AIAA-95-1729-CP

  6. Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3(3):233–260

    Article  MATH  Google Scholar 

  7. Jameson A, Shankaran S, Martinelli L (2003) An unstructured adjoint method for transonic flows. AIAA paper, 16th AIAA CFD Conference Orlando

  8. Jameson A (2003) Aerodynamic shape optimization using the adjoint method, 11–14. Department of Aeronautics and Astronautics Stanford University, Von Karman Institute Brussels

  9. Othmer C (2008) A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. Int J Numer Methods Fluids 58:861–877

    Article  MathSciNet  MATH  Google Scholar 

  10. Soto O, Löhner R (2004) On the computation of flow sensitivities from boundary integrals. In: 42nd AIAA aerospace sciences meeting and exhibit, Reno, NV

  11. Quarteroni A, Rozza G (2003) Optimal control and shape optimization of aorto-coronaric bypass anastomoses. Math Models Methods Appl Sci 13(12):1801–1823

    Article  MathSciNet  MATH  Google Scholar 

  12. Lincke A, Rung T (2012) Adjoint-based Sensitivity Analysis for buoyancy-driven incompressible Navier–Stokes equations with heat transfer. In: Proceedings of 8th international conference on engineering computational technology

  13. Bazilevs Y, Hsu M-C, Bement MT (2013) Adjoint-based control of fluid–structure interaction for computational steering applications. Proc Comput Sci 18:1989–1998

    Article  Google Scholar 

  14. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction (methods and applications). Wiley, Hoboken

    Book  MATH  Google Scholar 

  15. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MathSciNet  MATH  Google Scholar 

  16. Tröltzsch F (2010) Optimal control of partial differential equations: theory, methods and applications. AMS, Providence

    Book  MATH  Google Scholar 

  17. Hinze M et al (2009) Optimization with PDE Constraints. Springer, Berlin

    MATH  Google Scholar 

  18. Degroote J, Bathe KJ, Vierendeels J (2009) Performance of a new partitioned procedure versus a monolithic procedure in fluid–structure interaction. Comput Struct 87:793–801

    Article  Google Scholar 

  19. www.openfoam.com. OpenFOAM is a registered trade mark of Silicon Graphics International Corp

  20. Issa RI (1986) Solution of the implicitly discretized fluid flow equations by operator-splitting. J Comput Phys 62(1):40–65

    Article  MathSciNet  MATH  Google Scholar 

  21. Düster A, Hartmann S, Rank E (2003) p-FEM applied to finite isotropic hyperelastic bodies. Comput Methods Appl Mech Eng 192:5147–5166

    Article  MATH  Google Scholar 

  22. Netz T, Düster A, Hartmann S (2013) High-Order finite elements compared to low-order mixed element formulations. ZAMM-Z Ang Math Mech 93:163–176

    Article  MathSciNet  MATH  Google Scholar 

  23. Radtke L, Larena-Avellaneda A, Debus ES, Düster A (2016) Convergence acceleration for partitioned simulations of the fluid-structure interaction in arteries. Comput Mech 57:901–920

    Article  MathSciNet  MATH  Google Scholar 

  24. König M, Radtke L, Düster A (2016) A flexible C++ framework for the partitioned solution of strongly coupled multifield problems. Comput Math Appl 72:1764–1789

    Article  MathSciNet  MATH  Google Scholar 

  25. Brändli S, Düster A (2012) A flexible multi-physics coupling interface for partitioned solution approaches. Proc Appl Math Mech 12:363–364

    Article  Google Scholar 

  26. Lincke A, Rung T, Hinze M (2014) An efficient line search technique and its application to adjoint topology optimization. In: 85th annual meeting international association of applied mathematics and mechanics (GAMM)

  27. Galvez M, Badilla L, Valencia A, Zarate A (2005) Non-Newtonian blood flow dynamics in a right internal carotid artery with a saccular aneurysm. Int J Numer Methods 50:751–764

    MATH  Google Scholar 

  28. Radtke L (2013) Ein partitionierter Ansatz zur Simulation der Fluid-Struktur-Interaktion an der Schnittstelle zu künstlichen Blutgefäßen und endoluminalen Gefäßstützen, Master thesis TU Hamburg-Harburg

Download references

Author information

Authors and Affiliations

  1. Numerical Structural Analysis with Application in Ship Technology (M-10), Hamburg University of Technology, Am Schwarzenberg Campus 4 C, 21073, Hamburg, Germany

    J. P. Heners, L. Radtke & A. Düster

  2. Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    M. Hinze

Authors
  1. J. P. Heners
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Radtke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Hinze
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Düster
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Heners.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heners, J.P., Radtke, L., Hinze, M. et al. Adjoint shape optimization for fluid–structure interaction of ducted flows. Comput Mech 61, 259–276 (2018). https://doi.org/10.1007/s00466-017-1465-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-017-1465-5

Keywords

Search

Navigation