[en] We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for general balance laws, thus adding design capability to a tool with a wide range of applicability. Design variables are introduced on designated surfaces using the knots of a 2D spline-based geometry representation, while gradients are computed from the adjoint solution using a difference approximation of residual perturbations. A suitable optimization algorithm, such as an in-house steepest descent or the Preconditioned Sequential Quadratic Programming (PSQP) approach from the pyOpt framework, is then employed to find an improved geometry. We present verification of the implementation, including drag or heat flux minimization in compressible flows, as well as inverse design.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Balis, Joachim ; Université de Liège - ULiège > Unités de recherche interfacultaires > Space sciences, Technologies and Astrophysics Research (STAR) ; VKI - Von Karman Institute for Fluid Dynamics [BE]
Jacobs, Frederik ; VKI - Von Karman Institute for Fluid Dynamics [BE]
May, Georg ; VKI - Von Karman Institute for Fluid Dynamics [BE]
Language :
English
Title :
Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Vassberg, J., Jameson, A., Industrial applications of aerodynamic shape optimization. VKI lecture series on optimization and multidisciplinary design, 2018, 10.35294/ls201804.vassberg2.
Jameson, A., Aerodynamic shape optimization using the adjoint method. VKI lecture series on aerodynamic drag prediction and reduction, 2003.
Gunzburger, M.D., Perspectives in flow control and optimization. 2002, Society for Industrial and Applied Mathematics.
Pironneau, O., On optimum design in fluid mechanics. J Fluid Mech 64 (1974), 97–110.
Wang, Z.J., Fidkowski, K., Abgrall, R., Bassi, F., Caraeni, D., Cary, A., Deconinck, H., Hartmann, R., Hillewaert, K., Huynh, H.T., et al. High-order CFD methods: current status and perspective. Internat J Numer Methods Fluids 72:8 (2013), 811–845, 10.1002/fld.3767.
Huynh, H.T., Wang, Z.J., Vincent, P.E., High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids. Comput & Fluids 98 (2014), 209–220, 10.1016/j.compfluid.2013.12.007.
Reed WH, Hill TR. Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479, 1973.
Cockburn, B., Gopalakrishnan, J., Lazarov, R., Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J Numer Anal 47:2 (2009), 1319–1365, 10.1137/070706616.
Nguyen, N.C., Peraire, J., Cockburn, B., A hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. J Comput Phys 230 (2011), 1147–1170, 10.1016/j.jcp.2010.10.032.
Peraire, J., Nguyen, N.C., Cockburn, B., A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations. 48th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, 2010, 10.2514/6.2010-363.
Nguyen, N.C., Peraire, J., An adaptive shock-capturing HDG method for compressible flows. 20th AIAA computational fluid dynamics conference, 2011, 10.2514/6.2011-3060.
Oikawa, I., A hybridized discontinuous Galerkin method with reduced stabilization. J Sci Comput 65 (2014), 327–340, 10.1007/s10915-014-9962-6.
Oikawa, I., Analysis of a reduced-order HDG method for the Stokes equations. J Sci Comput, 2015, 10.1007/s10915-015-0090-8.
Qiu, W., Shi, K., A superconvergent HDG method for the incompressible Navier–Stokes equations on general polyhedral meshes. IMA J Numer Anal 36:4 (2016), 1943–1967, 10.1093/imanum/drv067.
Jaust, A., Schütz, J., A temporally adaptive hybridized discontinuous Galerkin method for time-dependent compressible flows. Comput & Fluids 98 (2014), 177–185, 10.1016/j.compfluid.2014.01.019.
Fidkowski, K.J., A hybridized discontinuous Galerkin method on mapped deforming domains. Comput & Fluids 139 (2016), 80–91, 10.1016/j.compfluid.2016.04.004.
Woopen, M., Ludescher, T., May, G., A hybridized discontinuous Galerkin method for turbulent compressible flow. 44th AIAA fluid dynamics conference, 2014, 10.2514/6.2014-2783.
Terrana, S., Nguyen, N., Peraire, J., GPU-accelerated large eddy simulation of hypersonic flows. AIAA scitech 2020 forum, 2020, 10.2514/6.2020-1062.
Vila-Pérez, J., Giacomini, M., Sevilla, R., Huerta, A., Hybridisable discontinuous Galerkin formulation of compressible flows. Arch Comput Methods Eng, 28, 2020, 10.1007/s11831-020-09508-z.
Cockburn, B., Hybridizable discontinuous Galerkin methods for second-order elliptic problems: overview, a new result and open problems. Jpn J Ind Appl Math, 40, 2023, 10.1007/s13160-023-00603-9.
Giacomini, M., An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations. J Sci Comput 75:1 (2018), 560–595, 10.1007/s10915-017-0545-1.
Wang, K., Yu, S., Wang, Z., Feng, R., Liu, T., Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method. Comput Methods Appl Mech Engrg 344 (2019), 602–625, 10.1016/j.cma.2018.10.033.
Fidkowski, K.J., Gradient-based shape optimization for unsteady turbulent simulations using field inversion and machine learning. Aerosp Sci Technol, 129, 2022, 107843, 10.1016/j.ast.2022.107843.
Sanjaya, D.P., Fidkowski, K., High-order node movement discretization error control in shape optimization. AIAA scitech forum 2023, 2023, 10.2514/6.2023-2367.
Coppeans, A., Fidkowski, K., Martins, J.R., Comparison of finite volume and high order discontinuous Galerkin based aerodynamic shape optimization. AIAA scitech forum 2023, 2023, 10.2514/6.2023-1845.
Woopen, M., Balan, A., May, G., Schütz, J., A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow. Comput & Fluids 98 (2014), 3–16, 10.1016/j.compfluid.2014.03.023.
Woopen, M., May, G., Schütz, J., Adjoint-based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods. Internat J Numer Methods Fluids 76:11 (2014), 811–834, 10.1002/fld.3959.
Balan, A., Woopen, M., May, G., Adjoint-based hp -adaptivity on anisotropic meshes for high-order compressible flow simulations. Comput & Fluids 139 (2016), 47–67, 10.1016/j.compfluid.2016.03.029.
Schütz, J., May, G., An adjoint consistency analysis for a class of hybrid mixed methods. IMA J Numer Anal 34:3 (2014), 1222–1239, 10.1093/imanum/drt036.
May, G., Hybridized discontinuous Galerkin methods : Formulation and discrete adjoint. VKI 38th lecture series on advanced computational fluid dynamics, 2015, 1–21.
Schöberl, J., NETGEN An advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci 1:1 (1997), 41–52, 10.1007/s007910050004.
Scoggins, J.B., Magin, T.E., Development of mutation++ : Multicomponent thermodynamic and transport properties for ionized plasmas written in C++. 11th AIAA/ASME joint thermophysics and heat transfer conference, 2014, 10.2514/6.2014-2966.
Balis, J., Jacobs, F., May, G., Aerodynamic shape optimization with hybridized discontinuous Galerkin schemes. AIAA scitech forum 2023, 2023, 10.2514/6.2023-1422.
Woopen, M., Balan, A., May, G., A unifying computational framework for adaptive high-order finite element methods. 22nd AIAA computational fluid dynamics conference, 2015, 10.2514/6.2015-2601.
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D., Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39:5 (2002), 1749–1779, 10.1137/s0036142901384162.
Hartmann, R., Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier–Stokes equations. Internat J Numer Methods Fluids 51:9–10 (2006), 1131–1156, 10.1002/fld.1134.
May, G., Devesse, K., Rangarajan, A., Magin, T., A hybridized discontinuous Galerkin solver for high-speed compressible flow. Aerospace, 8(11), 2021, 322, 10.3390/aerospace8110322.
Gangl, P., Sturm, K., Neunteufel, M., Schöberl, J., Fully and semi-automated shape differentiation in NGSolve. Struct Multidiscip Optim 63:3 (2020), 1579–1607, 10.1007/s00158-020-02742-w.
Yang, Z., Mavriplis, D.J., Mesh deformation strategy optimized by the adjoint method on unstructured meshes. AIAA J 45:12 (2007), 2885–2896, 10.2514/1.30592.
Luke, E., Collins, E., Blades, E., A fast mesh deformation method using explicit interpolation. J Comput Phys 231:2 (2012), 586–601, 10.1016/j.jcp.2011.09.021.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
