×

A partitioned scheme for adjoint shape sensitivity analysis of fluid-structure interactions involving non-matching meshes. (English) Zbl 07595253

Summary: This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration due to the mixed Lagrangian-Eulerian formulation of large-deformation FSI in this work. The adjoint FSI problem is partitioned as an assembly of well-known adjoint fluid and structural problems. The sub-adjoint problems are coupled with each other by augmenting the target functions with auxiliary functions, independent of the concrete choice of the underlying adjoint formulations. The auxiliary functions are linear force-based or displacement-based functionals which are readily available in well-established single-disciplinary adjoint solvers. Adjoint structural displacements, adjoint fluid displacements, and domain-based adjoint sensitivities of the fluid are the coupling fields to be exchanged between the adjoint solvers. A reduced formulation is also derived for the case of boundary-based adjoint shape sensitivity analysis for fluids. Numerical studies show that the complete formulation computes accurate shape gradients whereas inaccuracies appear in the reduced gradients. Mapping techniques including nearest element interpolation and the mortar method are studied in computational adjoint FSI. It is numerically shown that the mortar method does not introduce spurious oscillations in primal and sensitivity fields along non-matching interfaces.

MSC:

65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Software:

GitHub; SU2; OpenMDAO; KRATOS
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Albring, T.A., Sagebaum, M., and Gauger, N.R., Development of a consistent discrete adjoint solver in an evolving aerodynamic design framework, in 16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2015, p. 3240.
[2] Albring, T., Sagebaum, M., and Gauger, N.R., A consistent and robust discrete adjoint solver for the su2 framework-Validation and application, in New Results in Numerical and Experimental Fluid Mechanics X, Springer, 2016, pp. 77-86.
[3] Anderson, W. K.; Venkatakrishnan, V., Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation, Comput. Fluids., 28, 443-480 (1999) · Zbl 0968.76074 · doi:10.1016/S0045-7930(98)00041-3
[4] Barcelos, M.; Bavestrello, H.; Maute, K., A Schur-Newton-Krylov solver for steady-state aeroelastic analysis and design sensitivity analysis, Methods in Applied Mechanics and Engineering Comput. Methods. Appl. Mech. Eng., 195, 2050-2069 (2006) · Zbl 1178.76309 · doi:10.1016/j.cma.2004.09.013
[5] Belytschko, T.; Liu, W. K.; Moran, B.; Elkhodary, K., Nonlinear Finite Elements for Continua and Structures (2013), John Wiley & Sons · Zbl 1279.74002
[6] Carnarius, A., Thiele, F., Oezkaya, E., and Gauger, N.R., Adjoint approaches for optimal flow control, in 5th Flow Control Conference, 2010, p. 5088.
[7] Carvalho, M.; Durst, F.; Pereira, J., Predictions and measurements of laminar flow over two-dimensional obstacles, Mathematical Modelling Appl. Math. Model., 11, 23-34 (1987) · doi:10.1016/0307-904X(87)90181-8
[8] Castro, C.; Lozano, C.; Palacios, F.; Zuazua, E., Systematic continuous adjoint approach to viscous aerodynamic design on unstructured grids, AIAA J., 45, 2125-2139 (2007) · doi:10.2514/1.24859
[9] Dadvand, P.; Rossi, R.; Oñate, E., An object-oriented environment for developing finite element codes for multi-disciplinary applications, Archives Comput. Methods Engin., 17, 253-297 (2010) · Zbl 1360.76130 · doi:10.1007/s11831-010-9045-2
[10] de Boer, A.; van Zuijlen, A. H.; Bijl, H., Comparison of conservative and consistent approaches for the coupling of non-matching meshes, Comput. Methods. Appl. Mech. Eng., 197, 4284-4297 (2008) · Zbl 1194.74559 · doi:10.1016/j.cma.2008.05.001
[11] Degroote, J.; Haelterman, R.; Annerel, S.; Bruggeman, P.; Vierendeels, J., Performance of partitioned procedures in fluid-structure interaction, Structures Comput. Struct., 88, 446-457 (2010) · doi:10.1016/j.compstruc.2009.12.006
[12] Deparis, S., Numerical analysis of axisymmetric flows and methods for fluid-structure interaction arising in blood flow simulation, Tech. Rep., EPFL, 2004.
[13] Dettmer, W.; Perić, D., A computational framework for fluid-structure interaction: Finite element formulation and applications, Comput. Methods. Appl. Mech. Eng., 195, 5754-5779 (2006) · Zbl 1155.76354 · doi:10.1016/j.cma.2005.10.019
[14] Economon, T. D.; Palacios, F.; Copeland, S. R.; Lukaczyk, T. W.; Alonso, J. J., Su2: An open-source suite for multiphysics simulation and design, Aiaa J., 54, 828-846 (2015) · doi:10.2514/1.J053813
[15] EMPIRE, Enhanced multi physics interface research engine, 2018. Available at https://github.com/DrStS/EMPIRE-Core.
[16] Farhat, C.; Lesoinne, M.; Le Tallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity, Methods in Applied Mechanics and Engineering Comput. Methods. Appl. Mech. Eng., 157, 95-114 (1998) · Zbl 0951.74015 · doi:10.1016/S0045-7825(97)00216-8
[17] Fazzolari, A.; Gauger, N. R.; Brezillon, J., Efficient aerodynamic shape optimization in mdo context, J. Comput. Appl. Math., 203, 548-560 (2007) · Zbl 1111.76045 · doi:10.1016/j.cam.2006.04.013
[18] Felippa, C. A.; Park, K.; Farhat, C., Partitioned analysis of coupled mechanical systems, Methods in Applied Mechanics and Engineering Comput. Methods. Appl. Mech. Eng., 190, 3247-3270 (2001) · Zbl 0985.76075 · doi:10.1016/S0045-7825(00)00391-1
[19] Gray, J. S.; Hwang, J. T.; Martins, J. R.; Moore, K. T.; Naylor, B. A., Openmdao: An open-source framework for multidisciplinary design, analysis, and optimization, Struct. Multidiscipl. Optim., 59, 1075-1104 (2019) · doi:10.1007/s00158-019-02211-z
[20] Haubner, J.; Ulbrich, M.; Ulbrich, S., Analysis of shape optimization problems for unsteady fluid-structure interaction, Inverse. Probl., 36 (2020) · Zbl 1440.49044 · doi:10.1088/1361-6420/ab5a11
[21] Heners, J. P.; Radtke, L.; Hinze, M.; Düster, A., Adjoint shape optimization for fluid-structure interaction of ducted flows, Comput. Mech., 61, 259-276 (2018) · Zbl 1461.76152 · doi:10.1007/s00466-017-1465-5
[22] Hetu, J. F.; Pelletier, D. H., Fast, adaptive finite element scheme for viscous incompressible flows, AIAA J., 30, 2677-2682 (1992) · Zbl 0762.76054 · doi:10.2514/3.11284
[23] Jenkins, N.; Maute, K., An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems, Struct. Multidiscipl. Optim., 54, 1191-1208 (2016) · doi:10.1007/s00158-016-1467-5
[24] Kavvadias, I.; Papoutsis-Kiachagias, E.; Giannakoglou, K. C., On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization, J. Comput. Phys., 301, 1-18 (2015) · Zbl 1349.76616 · doi:10.1016/j.jcp.2015.08.012
[25] Kenway, G. K.; Kennedy, G. J.; Martins, J. R., Scalable parallel approach for high-fidelity steady-state aeroelastic analysis and adjoint derivative computations, AIAA J., 52, 935-951 (2014) · doi:10.2514/1.J052255
[26] Kiviaho, J.F., Jacobson, K., Smith, M.J., and Kennedy, G., A robust and flexible coupling framework for aeroelastic analysis and optimization, in 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2017, p. 4144.
[27] Kratos Development Team, The Kratos multiphysics open-source project, 2018. Available at https://github.com/KratosMultiphysics.
[28] Lozano, C., On mesh sensitivities and boundary formulas for discrete adjoint-based gradients in inviscid aerodynamic shape optimization, J. Comput. Phys., 346, 403-436 (2017) · Zbl 1378.76098 · doi:10.1016/j.jcp.2017.06.025
[29] Lozano, C., Singular and discontinuous solutions of the adjoint euler equations, AIAA J., 56, 4437-4452 (2018) · doi:10.2514/1.J056523
[30] Lozano, C., Watch your adjoints! lack of mesh convergence in inviscid adjoint solutions, AIAA J., 57, 9, 1-16 (2019) · doi:10.2514/1.J057259
[31] Lund, E.; Møller, H.; Jakobsen, L. A., Shape design optimization of stationary fluid-structure interaction problems with large displacements and turbulence, Struct. Multidiscipl. Optim., 25, 383-392 (2003) · doi:10.1007/s00158-003-0288-5
[32] Mani, K.; Mavriplis, D. J., Adjoint-based sensitivity formulation for fully coupled unsteady aeroelasticity problems, AIAA J., 47, 1902-1915 (2009) · doi:10.2514/1.40582
[33] Marcelet, M.; Peter, J.; Carrier, G., Sensitivity analysis of a strongly coupled aero-structural system using the discrete direct and adjoint methods, Euro. J. Comput. Mech./Revue Européenne De Mécanique Numérique, 17, 1077-1106 (2008) · Zbl 1292.74033 · doi:10.3166/remn.17.1077-1106
[34] Martins, J. R.; Hwang, J. T., Review and unification of methods for computing derivatives of multidisciplinary computational models, AIAA J., 51, 2582-2599 (2013) · doi:10.2514/1.J052184
[35] Maute, K.; Nikbay, M.; Farhat, C., Coupled analytical sensitivity analysis and optimization of three-dimensional nonlinear aeroelastic systems, AIAA J., 39, 2051-2061 (2001) · doi:10.2514/2.1227
[36] Mok, D.; Wall, W.; Ramm, E., Accelerated iterative substructuring schemes for instationary fluid-structure interaction, Comput. Fluid Solid Mech, 2, 1325-1328 (2001) · doi:10.1016/B978-008043944-0/50907-0
[37] Najian Asl, R., Shape optimization and sensitivity analysis of fluids, structures, and their interaction using vertex morphing parametrization, Dissertation, Technische Universität München, München, 2019.
[38] Palacios, F., Economon, T.D., and Alonso, J.J., Large-scale aircraft design using SU2, in 53rd AIAA Aerospace Sciences Meeting, 2015, p. 1946.
[39] RA Martins, J. R.; Alonso, J. J.; Reuther, J. J., High-fidelity aerostructural design optimization of a supersonic business jet, J. Aircr., 41, 523-530 (2004) · doi:10.2514/1.11478
[40] Richter, T., Goal-oriented error estimation for fluid-structure interaction problems, Comput. Methods. Appl. Mech. Eng., 223, 28-42 (2012) · Zbl 1253.74037 · doi:10.1016/j.cma.2012.02.014
[41] Sanchez, R.; Albring, T.; Palacios, R.; Gauger, N.; Economon, T.; Alonso, J., Coupled adjoint-based sensitivities in large-displacement fluid-structure interaction using algorithmic differentiation, Int. J. Numer. Methods. Eng., 113, 1081-1107 (2018) · doi:10.1002/nme.5700
[42] Sicklinger, S.; Belsky, V.; Engelmann, B.; Elmqvist, H.; Olsson, H.; Wüchner, R.; Bletzinger, K. U., Interface Jacobian-based co-simulation, Numerical Methods in Engineering Int. J. Numer. Methods. Eng., 98, 418-444 (2014) · Zbl 1352.65143 · doi:10.1002/nme.4637
[43] Singhammer, K.F., Optimal control of stationary fluid-structure interaction with partitioned methods, Dissertation, Technische Universität München, München, 2019.
[44] Stavropoulou, E., Sensitivity analysis and regularization for shape optimization of coupled problems, Ph.D. diss., Technische Universität München, 2015.
[45] SU2, Stanford University unstructured, 2018. Available at https://su2code.github.io.
[46] Tezduyar, T. E.; Mittal, S.; Ray, S.; Shih, R., Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Comput. Methods. Appl. Mech. Eng., 95, 221-242 (1992) · Zbl 0756.76048 · doi:10.1016/0045-7825(92)90141-6
[47] Wang, T., Development of co-simulation environment and mapping algorithms, Ph.D. diss., Technische Universität München, 2016.
[48] Wang, T.; Wüchner, R.; Sicklinger, S.; Bletzinger, K. U., Assessment and improvement of mapping algorithms for non-matching meshes and geometries in computational FSI, Comput. Mech., 57, 793-816 (2016) · Zbl 1382.74142 · doi:10.1007/s00466-016-1262-6
[49] Zhang, Z. J.; Khosravi, S.; Zingg, D. W., High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement, Struct. Multidiscipl. Optim., 55, 1217-1235 (2017) · doi:10.1007/s00158-016-1562-7
[50] Zhang, Z. J.; Zingg, D. W., Efficient monolithic solution algorithm for high-fidelity aerostructural analysis and optimization, AIAA J., 56, 1251-1265 (2017) · doi:10.2514/1.J056163
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.