Adjoint methods for car aerodynamics

The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence of the computational cost from the number of design variables that makes it particularly attractive for problems with large design spaces. O...

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Veröffentlicht in:	Journal of mathematics in industry Jg. 4; H. 1; S. 6
1. Verfasser:	Othmer, Carsten
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2014 Springer Nature B.V
Schlagworte:	Applications of Mathematics Automobile industry Design ECMI2012-Selected papers on Mathematics in Industry Math. Appl. in Environmental Science Mathematical and Computational Biology Mathematical and Computational Engineering Mathematical Methods in Physics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Methods Navier-Stokes equations Permeability Software Ventilation Viscosity Drag Reduction Adjoint Method Computational Fluid Dynamics Topology Optimisation Shape Optimisation
ISSN:	2190-5983, 2190-5983
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Abstract	The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence of the computational cost from the number of design variables that makes it particularly attractive for problems with large design spaces. Originally developed by Lions and Pironneau in the 70’s, the adjoint method has evolved towards a standard tool within the development processes of the aeronautical industries. Its uptake in the automotive industry, however, lags behind. The first systematic applications of adjoint methods in automotive CFD have interestingly not taken place in the classical shape design arena, but in a relatively young discipline of sensitivity-based optimisation: fluid dynamic topology optimisation. While being an established concept in structure mechanics for decades already, its transfer to fluid dynamics took place just ten years ago. We demonstrate that specifically for ducted flow applications, like airducts for cabin ventilation or engine intake ports, it constitutes a very powerful tool and has matured over the last years to a level that allows its systematic usage for various automotive applications. To drive adjoint-based shape optimisation to the same degree of maturity and robustness for car applications is the subject of ongoing research collaborations between academia and the car industry. Achievements and challenges encountered during these efforts are presented.
AbstractList	The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence of the computational cost from the number of design variables that makes it particularly attractive for problems with large design spaces. Originally developed by Lions and Pironneau in the 70's, the adjoint method has evolved towards a standard tool within the development processes of the aeronautical industries. Its uptake in the automotive industry, however, lags behind. The first systematic applications of adjoint methods in automotive CFD have interestingly not taken place in the classical shape design arena, but in a relatively young discipline of sensitivity-based optimisation: fluid dynamic topology optimisation. While being an established concept in structure mechanics for decades already, its transfer to fluid dynamics took place just ten years ago. We demonstrate that specifically for ducted flow applications, like airducts for cabin ventilation or engine intake ports, it constitutes a very powerful tool and has matured over the last years to a level that allows its systematic usage for various automotive applications. To drive adjoint-based shape optimisation to the same degree of maturity and robustness for car applications is the subject of ongoing research collaborations between academia and the car industry. Achievements and challenges encountered during these efforts are presented.
Author	Othmer, Carsten
Author_xml	– sequence: 1 givenname: Carsten surname: Othmer fullname: Othmer, Carsten email: carsten.othmer@volkswagen.de organization: Vehicle Technology, Group Research
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Cites_doi	10.1017/S0022112074002023 10.1504/IJAD.2011.038846 10.1002/fld.426 10.1007/978-3-540-71439-2_15 10.1002/fld.1770 10.1007/s00158-004-0508-7 10.1137/080727890 10.1080/0305215X.2012.717074 10.1016/j.compfluid.2008.12.006 10.1016/j.jcp.2010.03.037 10.1007/BF01061285
ContentType	Journal Article
Copyright	Othmer; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Author(s) 2014
Copyright_xml	– notice: Othmer; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. – notice: The Author(s) 2014
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References	Hinterberger C, Olesen M: Automatic geometry optimization of exhaust systems based on sensitivities computed by a continuous adjoint CFD method in OpenFOAM. SAE Technical Paper 2010–01–1278 2010. CarnariusAThieleFÖzkayaENemiliAGaugerNOptimal control of unsteady flows using a discrete and a continuous adjoint approachProceedings of the 25th Conference on System Modeling and Optimization, Berlin, Germany2011318327 ZymarisASPapadimitriouDIGiannakoglouKCOthmerCOptimal location of suction or blowing jets using the continuous adjoint approachProceedings of the 5th European Conf. on Computational Fluid Dynamics, Lisbon, Portugal, ECCOMAS CFD2010 ZymarisASPapadimitriouDIGiannakoglouKCOthmerCContinuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flowsComput Fluids2009388152815381242.7606410.1016/j.compfluid.2008.12.006 Torbert S, Löhner R: Checkpointing schemes for adjoint methods and strongly unsteady flow. AIAA-2012–0572 2012. OpenFOAM® - The Open Source CFD Toolbox [http://www.openfoam.com] ANSA® pre-processor – BETA CAE Systems S.A. [http://www.beta-cae.gr/ansa.htm] ANSA® pre-processor – BETA CAE Systems S.A. [http://www.beta-cae.gr/ansa.htm] JamesonAAerodynamic design via control theoryJ Sci Comput198832332600676.7605510.1007/BF01061285 JakubekDWagnerCShape optimization of train head cars using adjoint-based computational fluid dynamicsProceedings of the First International Conference on Railway Technology, Las Palmas de Gran Canaria, Spain2012 BorrvallTPeterssonJTopology optimization of fluids in Stokes flowInt J Numer Methods Fluids200341771071025.76007194958510.1002/fld.426 Gersborg-HansenASigmundOHaberRTopology optimization of channel flow problemsStruct Multidiscip Optim2005301811921243.76034216571910.1007/s00158-004-0508-7 Towara M: Numerical optimization of an oil intake duct with adjoint topological methods. Diploma thesis. RWTH Aachen University, Dept. of Software and Tools for Computational Engineering; 2011. HeinemannTSpringerMLienhartHKniesburgesSBeckerSActive flow control on a 1:4 car modelProceedings of the 16th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal2012 OthmerCGrahsTApproaches to fluid dynamic optimization in the car development processProceedings of the EUROGEN Conference, Munich, Germany2005 Islam M, Decker F, de Villiers E, Jackson A, Gines J, Grahs T, Gitt-Gehrke A, Comas i Font J: Application of detached-Eddy simulation for automotive aerodynamics development. SAE Technical Paper 2009–01–0333 2009. BrunnAWassenESperberDNitscheWThieleFActive drag control for a generic car modelNotes Numer Fluid Mech Multidiscipl Des20079524725910.1007/978-3-540-71439-2_15 Löhner R, Soto O, Yang C: An adjoint-based design methodology for CFD optimization problems. AIAA-03–0299 2003. HinterbergerCOlesenMIndustrial application of continuous adjoint flow solvers for the optimization of automotive exhaust systemsProceedings of the ECCOMAS Thematic Conf. - CFD & Optimization, Antalya, Turkey, ECCOMAS2011 Moos O, Klimetzek F, Rossmann R: Bionic optimization of air-guiding systems. SAE Technical Paper 2004–01–1377 2004. Moos O, Klimetzek F, Rossmann R: Bionic optimization of air-guiding systems. SAE Technical Paper 2004-01-1377 2004. de Villiers E, Othmer C: Multi-objective adjoint optimization of intake port geometry. SAE Technical Paper 2012–01–0905 2012. PironneauOOn optimum design in fluid mechanicsJ Fluid Mech197464971100281.7602034722910.1017/S0022112074002023 OthmerCA continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flowsInt J Numer Methods Fluids2008588618771152.76025246428410.1002/fld.1770 OthmerCPapoutsis-KiachagiasEMHaliskosKCFD optimization via sensitivity-based shape morphingProceedings of the 4th ANSA & μETA Internat. Conf., Thessaloniki, Greece, BETA CAE Systems S.A2011 aboutFlow - Adjoint-based optimisation of industrial and unsteady flows [http://aboutflow.sems.qmul.ac.uk] LinckeARungTAdjoint-based sensitivity analysis for Buoyancy-driven incompressible Navier-Stokes equations with heat transferProceedings of the Eighth Internat. Conf. on Engineering Computational Technology, Dubrovnik, Croatia2012 WangQMoinPIaccarinoGMinimal repetition dynamic checkpointing algorithm for unsteady adjoint calculationSIAM J Sci Comput2009314254925671196.65050252028910.1137/080727890 Petzold R: Experimentelle Untersuchungen zur Strömungsbeeinflussung an einem 1:4-Fahrzeugmodell. Diploma thesis. TU Braunschweig, Inst. für Strömungsmechanik; 2011. BendsoeMPSigmundOTopology Optimization: Theory, Methods and Applications2004BerlinSpringer10.1007/978-3-662-05086-6 GriewankAAchieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiationOptim Methods Softw19921335410.1080/10556789208805505 ZymarisASPapadimitriouDIGiannakoglouKCOthmerCAdjoint wall functions: a new concept for use in aerodynamic shape optimizationJ Comput Phys2010229135228524505762206264365210.1016/j.jcp.2010.03.037 Othmer C, de Villiers E, Weller HG: Implementation of a continuous adjoint for topology optimization of ducted flows. AIAA-2007–3947 2007. Economon TD, Palacios F, Alonso JJ: A coupled-adjoint method for aerodynamic and aeroacoustic optimization. AIAA-2012–5598 2012. LionsJLOptimal Control of Systems Governed by Partial Differential Equations1971New YorkSpringer0203.0900110.1007/978-3-642-65024-6 KontoleontosEAPapoutsis-KiachagiasEMZymarisASPapadimitriouDIGiannakoglouKCAdjoint-based constrained topology optimization for viscous flows, including heat transferEng Optim2013458941961317077010.1080/0305215X.2012.717074 GiannakoglouKCContinuous adjoint methods in shape, topology, flow-control and robust optimizationOpen Source CFD International Conference, London, UK, ICON-CFD2012 Stavropoulou E, Hojjat M, Bletzinger KU: In-plane mesh regularization for node-based shape optimization problems. Comput Methods Appl Mech Eng, in press [http://www.sciencedirect.com/science/article/pii/S004578251400070X] Nadarajah S, Jameson A: A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. AIAA-00–0667 2000. Ahmed SR, Ramm R, Falting G: Some salient features of the time-averaged ground vehicle wake. SAE Technical Paper 84–0300 1984. BideauxEBobillierPFournierEGillieronPEl HajemMChampagneJYGilottePKourtaADrag reduction by pulsed jets on strongly unstructured wake: towards the square back controlInt J Aerodyn201113/428229810.1504/IJAD.2011.038846 HojjatMStavropoulouEBletzingerKUThe vertex morphing method for node-based shape optimizationComput Methods Appl Mech Eng20142684945131295.74082313350910.1016/j.cma.2013.10.015 HelgasonEKrajnovicSAerodynamic shape optimization of a pipe using the adjoint methodProceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, Texas, USA, IMECE2012 OthmerCKaminskiTGieringRComputation of topological sensitivities in fluid dynamics: cost function versatilityProceedings of the ECCOMAS CFD Conference, Delft, The Netherlands2006 -
References_xml	– reference: JamesonAAerodynamic design via control theoryJ Sci Comput198832332600676.7605510.1007/BF01061285 – reference: Moos O, Klimetzek F, Rossmann R: Bionic optimization of air-guiding systems. SAE Technical Paper 2004–01–1377 2004. Moos O, Klimetzek F, Rossmann R: Bionic optimization of air-guiding systems. SAE Technical Paper 2004-01-1377 2004. – reference: Towara M: Numerical optimization of an oil intake duct with adjoint topological methods. Diploma thesis. RWTH Aachen University, Dept. of Software and Tools for Computational Engineering; 2011. – reference: PironneauOOn optimum design in fluid mechanicsJ Fluid Mech197464971100281.7602034722910.1017/S0022112074002023 – reference: Hinterberger C, Olesen M: Automatic geometry optimization of exhaust systems based on sensitivities computed by a continuous adjoint CFD method in OpenFOAM. SAE Technical Paper 2010–01–1278 2010. – reference: OthmerCGrahsTApproaches to fluid dynamic optimization in the car development processProceedings of the EUROGEN Conference, Munich, Germany2005 – reference: ZymarisASPapadimitriouDIGiannakoglouKCOthmerCAdjoint wall functions: a new concept for use in aerodynamic shape optimizationJ Comput Phys2010229135228524505762206264365210.1016/j.jcp.2010.03.037 – reference: OpenFOAM® - The Open Source CFD Toolbox [http://www.openfoam.com] – reference: BideauxEBobillierPFournierEGillieronPEl HajemMChampagneJYGilottePKourtaADrag reduction by pulsed jets on strongly unstructured wake: towards the square back controlInt J Aerodyn201113/428229810.1504/IJAD.2011.038846 – reference: BorrvallTPeterssonJTopology optimization of fluids in Stokes flowInt J Numer Methods Fluids200341771071025.76007194958510.1002/fld.426 – reference: JakubekDWagnerCShape optimization of train head cars using adjoint-based computational fluid dynamicsProceedings of the First International Conference on Railway Technology, Las Palmas de Gran Canaria, Spain2012 – reference: BrunnAWassenESperberDNitscheWThieleFActive drag control for a generic car modelNotes Numer Fluid Mech Multidiscipl Des20079524725910.1007/978-3-540-71439-2_15 – reference: Gersborg-HansenASigmundOHaberRTopology optimization of channel flow problemsStruct Multidiscip Optim2005301811921243.76034216571910.1007/s00158-004-0508-7 – reference: LionsJLOptimal Control of Systems Governed by Partial Differential Equations1971New YorkSpringer0203.0900110.1007/978-3-642-65024-6 – reference: HelgasonEKrajnovicSAerodynamic shape optimization of a pipe using the adjoint methodProceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, Texas, USA, IMECE2012 – reference: GiannakoglouKCContinuous adjoint methods in shape, topology, flow-control and robust optimizationOpen Source CFD International Conference, London, UK, ICON-CFD2012 – reference: OthmerCA continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flowsInt J Numer Methods Fluids2008588618771152.76025246428410.1002/fld.1770 – reference: WangQMoinPIaccarinoGMinimal repetition dynamic checkpointing algorithm for unsteady adjoint calculationSIAM J Sci Comput2009314254925671196.65050252028910.1137/080727890 – reference: CarnariusAThieleFÖzkayaENemiliAGaugerNOptimal control of unsteady flows using a discrete and a continuous adjoint approachProceedings of the 25th Conference on System Modeling and Optimization, Berlin, Germany2011318327 – reference: HinterbergerCOlesenMIndustrial application of continuous adjoint flow solvers for the optimization of automotive exhaust systemsProceedings of the ECCOMAS Thematic Conf. - CFD & Optimization, Antalya, Turkey, ECCOMAS2011 – reference: HeinemannTSpringerMLienhartHKniesburgesSBeckerSActive flow control on a 1:4 car modelProceedings of the 16th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal2012 – reference: Torbert S, Löhner R: Checkpointing schemes for adjoint methods and strongly unsteady flow. AIAA-2012–0572 2012. – reference: Löhner R, Soto O, Yang C: An adjoint-based design methodology for CFD optimization problems. AIAA-03–0299 2003. – reference: Stavropoulou E, Hojjat M, Bletzinger KU: In-plane mesh regularization for node-based shape optimization problems. Comput Methods Appl Mech Eng, in press [http://www.sciencedirect.com/science/article/pii/S004578251400070X] – reference: BendsoeMPSigmundOTopology Optimization: Theory, Methods and Applications2004BerlinSpringer10.1007/978-3-662-05086-6 – reference: Economon TD, Palacios F, Alonso JJ: A coupled-adjoint method for aerodynamic and aeroacoustic optimization. AIAA-2012–5598 2012. – reference: ZymarisASPapadimitriouDIGiannakoglouKCOthmerCContinuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flowsComput Fluids2009388152815381242.7606410.1016/j.compfluid.2008.12.006 – reference: OthmerCPapoutsis-KiachagiasEMHaliskosKCFD optimization via sensitivity-based shape morphingProceedings of the 4th ANSA & μETA Internat. Conf., Thessaloniki, Greece, BETA CAE Systems S.A2011 – reference: ZymarisASPapadimitriouDIGiannakoglouKCOthmerCOptimal location of suction or blowing jets using the continuous adjoint approachProceedings of the 5th European Conf. on Computational Fluid Dynamics, Lisbon, Portugal, ECCOMAS CFD2010 – reference: KontoleontosEAPapoutsis-KiachagiasEMZymarisASPapadimitriouDIGiannakoglouKCAdjoint-based constrained topology optimization for viscous flows, including heat transferEng Optim2013458941961317077010.1080/0305215X.2012.717074 – reference: HojjatMStavropoulouEBletzingerKUThe vertex morphing method for node-based shape optimizationComput Methods Appl Mech Eng20142684945131295.74082313350910.1016/j.cma.2013.10.015 – reference: aboutFlow - Adjoint-based optimisation of industrial and unsteady flows [http://aboutflow.sems.qmul.ac.uk] – reference: LinckeARungTAdjoint-based sensitivity analysis for Buoyancy-driven incompressible Navier-Stokes equations with heat transferProceedings of the Eighth Internat. Conf. on Engineering Computational Technology, Dubrovnik, Croatia2012 – reference: OthmerCKaminskiTGieringRComputation of topological sensitivities in fluid dynamics: cost function versatilityProceedings of the ECCOMAS CFD Conference, Delft, The Netherlands2006 – reference: Nadarajah S, Jameson A: A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. AIAA-00–0667 2000. – reference: ANSA® pre-processor – BETA CAE Systems S.A. [http://www.beta-cae.gr/ansa.htm] ANSA® pre-processor – BETA CAE Systems S.A. [http://www.beta-cae.gr/ansa.htm] – reference: Ahmed SR, Ramm R, Falting G: Some salient features of the time-averaged ground vehicle wake. 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Snippet	The adjoint method has long been considered as the tool of choice for gradient-based optimisation in computational fluid dynamics (CFD). It is the independence...
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SubjectTerms	Applications of Mathematics Automobile industry Design ECMI2012-Selected papers on Mathematics in Industry Math. Appl. in Environmental Science Mathematical and Computational Biology Mathematical and Computational Engineering Mathematical Methods in Physics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Methods Navier-Stokes equations Permeability Software Ventilation Viscosity
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Title	Adjoint methods for car aerodynamics
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