×

zbMATH — the first resource for mathematics

On mesh sensitivities and boundary formulas for discrete adjoint-based gradients in inviscid aerodynamic shape optimization. (English) Zbl 1378.76098
Summary: This paper shows how to obtain boundary formulas for discrete-adjoint-based sensitivities in shape optimization problems. The analysis is carried out for inviscid flows in two-dimensional, unstructured triangular grids. The new formulation agrees with known continuous adjoint boundary formulas for the sensitivities, and the derivation sheds light into the required approximations and the reasons for the equivalence (or lack thereof) between boundary and domain-based adjoint sensitivities. Alternative approximations are also discussed.

MSC:
76M30 Variational methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
49Q10 Optimization of shapes other than minimal surfaces
Software:
TAU
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Jameson, A., Aerodynamic design via control theory, J. Sci. Comput., 3, 3, 233-260, (1988) · Zbl 0676.76055
[2] Wang, G.; Xu, L.; Li, C.; Ye, Z.-Y., Influence of mesh sensitivities on computational-fluid-dynamics-based derivative calculation, AIAA J., 54, 12, 3717-3726, (2016)
[3] Nielsen, E.; Anderson, W., Recent improvements in aerodynamic design optimization on unstructured meshes, AIAA J., 40, 6, 1155-1163, (2002)
[4] Nielsen, E.; Park, M., Using an adjoint approach to eliminate mesh sensitivities in computational design, AIAA J., 44, 5, 948-953, (2006)
[5] 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
[6] Jameson, A.; Kim, S., Reduction of the adjoint gradient formula for aerodynamic shape optimization problems, AIAA J., 41, 11, 2114-2129, (2003)
[7] Soto, O.; Löhner, R., On the computation of flow sensitivities from boundary integrals, (2004), AIAA Paper 2004-0112
[8] Papadimitriou, D.; Giannakoglou, K., A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows, Comput. Fluids, 36, 2, 325-341, (2007) · Zbl 1177.76369
[9] Castro, C.; Lozano, C.; Palacios, F.; Zuazua, E., Systematic continuous adjoint approach to viscous aerodynamic design on unstructured grids, AIAA J., 45, 9, 2125-2139, (September 2007)
[10] Kavvadias, I.; Papoutsis-Kiachagias, E.; Giannakoglou, K., On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization, J. Comput. Phys., 301, 1-18, (15 November 2015)
[11] Lozano, C., Discrete surprises in the computation of sensitivities from boundary integrals in the continuous adjoint approach to inviscid aerodynamic shape optimization, Comput. Fluids, 56, 118-127, (2012) · Zbl 1365.76100
[12] Jameson, A., Optimum aerodynamic design using CFD and control theory, (1995), AIAA Paper 95-1729
[13] Lozano, C.; Andrés, E.; Martín, M.; Bitrián, P., Domain versus boundary computation of flow sensitivities with the continuous adjoint method for aerodynamic shape optimization problems, Int. J. Numer. Methods Fluids, 70, 10, 1305-1323, (2012) · Zbl 1412.49081
[14] Lozano, C., Adjoint viscous sensitivity derivatives with a reduced gradient formulation, AIAA J., 50, 1, 203-214, (2012)
[15] Nadarajah, S.; Jameson, A., A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization, (38th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, (2000)), AIAA Paper 2000-0667
[16] Barth, T., Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations, special course on unstructured methods for advection dominated flows, 6-1-6-61, (1991), AGARD Report No. 787, Section 6
[17] Nishikawa, H., Beyond interface gradient: a general principle for constructing diffusion schemes, (40th AIAA Fluid Dynamics Conference and Exhibit, Chicago, IL, (2010)), AIAA Paper 2010-5093
[18] Dwight, R.; Brezillon, J., Effect of approximations of the discrete adjoint on gradient-based optimization, AIAA J., 44, 12, 3022-3071, (2006)
[19] Peter, J.; Dwight, R. P., Numerical sensitivity analysis for aerodynamic optimization: a survey of approaches, Comput. Fluids, 39, 10, 373-391, (2010) · Zbl 1242.76301
[20] Hazra, S.; Jameson, A., One-shot pseudo-time method for aerodynamic shape optimization using the Navier-Stokes equations, Int. J. Numer. Methods Fluids, 68, 564-581, (2012) · Zbl 1335.76045
[21] Giles, M., Discrete adjoint approximations with shocks, (Hou, T.; Tadmor, E., Hyperbolic Problems: Theory, Numerics, Applications, (2003), Springer-Verlag), 185-194 · Zbl 1134.76396
[22] Baeza, A.; Castro, C.; Palacios, F.; Zuazua, E., 2-D Euler shape design on nonregular flows using adjoint rankine-hugoniot relations, AIAA J., 47, 3, 552-562, (2009)
[23] Schmidt, S.; Schulz, V.; Ilic, C.; Gauger, N., Three dimensional large scale aerodynamic shape optimization based on shape calculus, (41st AIAA Fluid Dynamics Conference and Exhibit, Honolulu, HI, June 27-30, (2011)), AIAA Paper 2011-3718
[24] Jameson, A.; Schmidt, W.; Turkel, E., Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, (AIAA 14th Fluid and Plasma Dynamic Conference, Palo Alto, CA, (June 1981)), AIAA Paper 81-1259
[25] Amoignon, O.; Pralits, J.; Hanifi, A.; Berggren, M.; Henningson, D., Shape optimization for delay of laminar-turbulent transition, AIAA J., 44, 5, 1009-1024, (2006)
[26] Schwamborn, D.; Gerhold, T.; Heinrich, R., The DLR TAU-code: recent applications in research and industry, (Proceedings of ECCOMAS CFD 2006, European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, (2006))
[27] Toulorge, T., Implementation of dynamic mesh feature into NENS2D, (2003), INTA Technical Report AT/TNO/4410/009/INTA/03
[28] Giles, M. B.; Pierce, N. A., Adjoint equations in CFD: duality, boundary conditions and solution behavior, (13th AIAA Computational Fluid Dynamics Conference, Snowmass Village, CO, June 29-July 2, (1997)), AIAA Paper 97-1850
[29] Leoviriyakit, K.; Jameson, A.; Kim, S., Viscous aerodynamic shape optimization of wings including planform variables, (21st Applied Aerodynamics Conference, Orlando, FL, June 23-26, (2003)), AIAA Paper 2003-3498
[30] Giles, M.; Ulbrich, S., Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws, part 1: linearized approximations and linearized output functionals, SIAM J. Numer. Anal., 48, 3, 882-904, (2010) · Zbl 1215.65146
[31] Giles, M.; Ulbrich, S., Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws, part 2: adjoint approximations and extensions, SIAM J. Numer. Anal., 48, 3, 905-921, (2010) · Zbl 1215.65147
[32] Nishikawa, H., Accuracy-preserving boundary flux quadrature for finite-volume discretization on unstructured grids, J. Comput. Phys., 281, 518-555, (2015) · Zbl 1352.65432
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.