Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics
Full Article - Open Access.
PARTITIONED SOLUTION OF THE UNSTEADY ADJOINT EQUATIONS FOR THE ONE-DIMENSIONAL FLOWIN A FLEXIBLE TUBE
For gradient-based optimization, the gradient of the objective function needs to be calculated repeatedly. If the number of design variables is high, this gradient can be obtained efficiently from adjoint equations. This research focuses on the gradient calculation for an objective function which involves a fluid-structure interaction (FSI) simulation. The interaction can be calculated in a partitioned way by coupling a flow solver with a structural solver. In this work, quasi-Newton coupling iterations with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS) are employed for the state equations as well as for their adjoint equations. The problem at hand is the unsteady, one-dimensional flow of an incompressible, inviscid fluid in an elastic tube. Special attention has been given to the interface variables which are exchanged between the adjoint flow and structural solver, to avoid the communication of system matrices between them.
Palavras-chave: Adjoint, Fluid-structure interaction, partitioned, quasi-Newton.,
-  R. Balasubramanian and J.C. Newman. Discrete direct and adjoint sensitivity analysis for arbitrary mach number flows. International Journal for Numerical Methods in Engineering, 66(2):297–318, 2006.
-  P. Causin, J.-F. Gerbeau, and F. Nobile. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering, 194(42–44):4506–4527, 2005.
-  G. Cowper. The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics, 33(2):335–340, 1966.
-  J. Degroote, S. Annerel, and J. Vierendeels. Stability analysis of Gauss-Seidel iterations in a partitioned simulation of fluid-structure interaction. Computers Andamp; Structures, 88(5– 6):263–270, 2010.
-  J. Degroote, K.-J. Bathe, and J. Vierendeels. Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction. Computers Andamp; Structures, 87(11–12):793–801, 2009.
-  J. Degroote, P. Bruggeman, R. Haelterman, and J. Vierendeels. Stability of a coupling technique for partitioned solvers in FSI applications. Computers Andamp; Structures, 86(23– 24):2224–2234, 2008.
-  J. Degroote, R. Haelterman, S. Annerel, P. Bruggeman, and J. Vierendeels. Performance of partitioned procedures in fluid-structure interaction. Computers Andamp; Structures, 88(7– 8):446–457, 2010.
-  C. Farhat, K.G. van der Zee, and P. Geuzaine. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Computer Methods in Applied Mechanics and Engineering, 195(17–18):1973–2001, 2006.
-  A. Fazzolari, N. Gauger, and J. Brezillon. Efficient aerodynamic shape optimization in MDO context. Journal of Computational and Applied Mathematics, 203(2):548–560, 2007.
-  C.A. Felippa, K.C. Park, and C. Farhat. Partitioned analysis of coupled mechanical systems. Computer Methods in Applied Mechanics and Engineering, 190(24–25):3247– 3270, 2001.
-  N. Gauger and A. Fazzolari. MegaDesign and MegaOpt - German Initiatives for Aerodynamic Simulation and Optimization in Aircraft Design, Results of the closing symposium of the MegaDesign and MegaOpt projects, Braunschweig, Germany, 23 - 24 May, 2007, volume 107 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, chapter Adjoint Methods for Coupled CFD-CSM Optimization, pages 237–246. Springer-Verlag, Berlin Heidelberg, 2009.
-  M. Gee, U. Küttler, and W.A. Wall. Truly monolithic algebraic multigrid for fluidstructure interaction. International Journal for Numerical Methods in Engineering, 85(8):987–1016, 2011.
-  J.-F. Gerbeau and M. Vidrascu. A quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows. ESAIM: Mathematical Modelling and Numerical Analysis, 37(4):631–648, 2003.
-  A. Griewank and A.Walther. Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differtiation. ACM Transactions on Mathematical Software, 26(1):19–45, 2000.
-  M. Heil. An efficient solver for the fully coupled solution of large-displacement fluidstructure interaction problems. Computer Methods in Applied Mechanics and Engineering, 193(1–2):1–23, 2004.
-  M. Hojjat, E. Stavropoulou, T. Gallinger, U. Israel, R. Wüchner, and K.-U. Bletzinger. Fluid-structure interaction in the context of shape optimization and computational wind engineering. In H.-J. Bungartz, M. Mehl, and M. Schäfer, editors, Fluid-Structure Interaction II: Modelling, Simulation, Optimization, Lecture Notes in Computational Science and Engineering, pages 351–381. Springer, Berlin Heidelberg, 2010.
-  B. Hübner, E. Walhorn, and D. Dinkler. A monolithic approach to fluid-structure interaction using space-time finite elements. Computer Methods in Applied Mechanics and Engineering, 193(23–26):2087–2104, 2004.
-  U. Küttler and W.A. Wall. Fixed-point fluid-structure interaction solvers with dynamic relaxation. Computational Mechanics, 43(1):61–72, 2008.
-  F. Li and Z. Sun. A finite difference scheme for solving the Timoshenko beam equations with boundary feedback. Journal of Computational and Applied Mathematics, 200(2):606–627, 2007.
-  J.R.R.A. Martins, J.J. Alonso, and J.J. Reuther. High-fidelity aerostructural design optimization of a supersonic business jet. Journal of Aircraft, 41(3):523–530, 2004.
-  J.R.R.A. Martins, J.J. Alonso, and J.J. Reuther. A coupled-adjoint sensitivity analysis method for high-fidelity aero-structural design. Optimization and Engineering, 6(1):33– 62, 2005.
-  K. Maute, M. Nikbay, and C. Farhat. Coupled analytical sensitivity analysis and optimization of three-dimensional nonlinear aeroelastic systems. American Institute of Aeronautics and Astronautics Journal, 39(11):2051–2061, 2001.
-  K. Maute, M. Nikbay, and C. Farhat. Sensitivity analysis and design optimization of three-dimensional nonlinear aeroelastic systems by the adjoint method. International Journal for Numerical Methods in Engineering, 56(6):911–933, 2003.
-  C. Michler, E.H. van Brummelen, and R. de Borst. An interface Newton-Krylov solver for fluid-structure interaction. International Journal for Numerical Methods in Fluids, 47(10-11):1189–1195, 2005.
-  D.P. Mok, W.A. Wall, and E. Ramm. Accelerated iterative substructuring schemes for instationary fluid-structure interaction. In K.-J. Bathe, editor, Computational Fluid and Solid Mechanics, pages 1325–1328. Elsevier, 2001.
-  E. Nielsen, B. Diskin, and N. Yamaleev. Discrete adjoint-based design optimization of unsteady turbulent flows on dynamic unstructured grids. In 19th AIAA Computational Fluid Dynamics Conference, pages 1–22, San Antonio, TX, USA, 22–25 June 2009. AIAA 2009-3802.
-  K. Palaniappan, P. Sahu, J. Alonso, and A. Jameson. Active flutter control using an adjoint method. In 44th AIAA Aerospace Sciences Meeting and Exhibit, pages 1–11, Reno, NV, USA, 9–12 January 2006. AIAA 2006-844.
-  K. Palaniappan, P. Sahu, J. Alonso, and A. Jameson. Design of adjoint based laws for wing flutter control. In 47th AIAA Aerospace Sciences Meeting, pages 1–20, Orlando, FL, USA, 5–8 January 2009. AIAA 2009-148.
-  D.I. Papadimitriou and K.C. Giannakoglou. Direct, adjoint and mixed approaches for the computation of hessian in airfoil design problems. International Journal for Numerical Methods in Fluids, 56(10):1929–1943, 2008.
-  A. Quarteroni, M. Tuveri, and A. Veneziani. Computational vascular fluid dynamics: problems, models and methods. Computing and Visualization in Science, 2(4):163–197, 2000.
-  M.P. Rumpfkeil and D.W. Zingg. The optimal control of unsteady flows with a discrete adjoint method. Optimization and Engineering, 11(1):5–22, 2010.
-  J. Sternberg and A. Griewank. Automatic Differentiation: Applications, Theory, and Implementations, volume 50 of Lecture Notes in Computational Science and Engineering, chapter Reduction of Storage Requirement by Checkpointing for Time-Dependent Optimal Control Problems in ODEs, pages 99–110. Springer-Verlag, Berlin Heidelberg, 2006.
-  A. Stück, F. Camelli, and R. Löhner. Adjoint-based design of passive and active shock mitigation devices. In 48th AIAA Aerospace Sciences Meeting, pages 1–30, Orlando, FL, USA, 4–7 January 2010. AIAA 2010-1430.
-  A. Stück, F. Camelli, and R. Löhner. Adjoint-based design of shock mitigation devices. International Journal for Numerical Methods in Fluids, 64(4):443–472, 2010.
-  E.H. van Brummelen. Added mass effects of compressible and incompressible flows in fluid-structure interaction. Journal of Applied Mechanics, 76(2):021206–1–7, 2009.
-  J. Vierendeels, K. Dumont, E. Dick, and P.R. Verdonck. Analysis and stabilization of fluid-structure interaction algorithm for rigid-body motion. AIAA Journal, 43(12):2549– 2557, 2005.
-  I. Vignon-Clementel, C. Figueroa, K. Jansen, and C. Taylor. Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries. Computer Methods in Biomechanics and Biomedical Engineering, 13(5):625– 640, 2010.
-  Q. Wang, P. Moin, and G. Iaccarino. Minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation. SIAM Journal on Scientific Computing, 31(4):2549–2567, 2009.
-  R. Wüchner, A. Kupzok, and K.-U. Bletzinger. A framework for stabilized partitioned analysis of thin membrane-wind interaction. International Journal for Numerical Methods in Fluids, 54(6–8):945–963, 2007.
Degroote, J.; Hojjat, M.; Stavropoulou, E.; Wüchner, R.; Bletzinger, K.-U.; "PARTITIONED SOLUTION OF THE UNSTEADY ADJOINT EQUATIONS FOR THE ONE-DIMENSIONAL FLOWIN A FLEXIBLE TUBE", p. 3814-3831 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1].
São Paulo: Blucher,
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19599
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