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Algorithm Developments for Discrete Adjoint Methods
, 2001
"... This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed ..."
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Cited by 50 (13 self)
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This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed
Approximation and Model Management in Aerodynamic Optimization with VariableFidelity Models
, 2001
"... This work discusses an approach, firstorder approximation and model management optimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lowerfidelity, cheaper models in iterative procedures with occasional, but syst ..."
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Cited by 40 (2 self)
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This work discusses an approach, firstorder approximation and model management optimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lowerfidelity, cheaper models in iterative procedures with occasional, but systematic, recourse to higherfidelity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is that it is globally convergent to a solution of the original, highfidelity problem. Variants of AMMO based on three nonlinear programming algorithms are demonstrated on a threedimensional aerodynamic wing optimization problem and a twodimensional airfoil optimization problem. Euler analysis on meshes of varying degrees of refinement provides a suite of variablefidelity models. Preliminary results indicate threefold savings in terms of highfidelity analyses for the threedimensional problem and twofold savings for the twodimensional problem.
Optimization With VariableFidelity Models Applied To Wing Design
, 2000
"... This work discusses an approach, the Approximation Management Framework (AMF), for solving optimization problems that involve computationally expensive simulations. AMF aims to maximize the use of lowerfidelity, cheaper models in iterative procedures with occasional, but systematic, recourse to high ..."
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Cited by 34 (2 self)
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This work discusses an approach, the Approximation Management Framework (AMF), for solving optimization problems that involve computationally expensive simulations. AMF aims to maximize the use of lowerfidelity, cheaper models in iterative procedures with occasional, but systematic, recourse to higherfidelity, more expensive models for monitoring the progress of the algorithm. The method is globally convergent to a solution of the original, highfidelity problem. Three versions of AMF, based on three nonlinear programming algorithms, are demonstrated on a 3D aerodynamic wing optimization problem and a 2D airfoil optimization problem. In both cases Euler analysis solved on meshes of various refinement provides a suite of variablefidelity models. Preliminary results indicate threefold savings in terms of highfidelity analyses in case of the 3D problem and twofold savings for the 2D problem. Key Words: Approximation concepts, approximation management, model management, surrogate optimi...
Analytic adjoint solutions for the quasionedimensional Euler equations
 J. Fluid Mechanics
, 2001
"... The analytic properties of adjoint solutions are examined for the quasionedimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is requir ..."
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Cited by 34 (9 self)
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The analytic properties of adjoint solutions are examined for the quasionedimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is required at the shock. A Green’s function approach is used to derive the analytic adjoint solutions corresponding to supersonic, subsonic, isentropic and shocked transonic flows in a converging–diverging duct of arbitrary shape. This analysis reveals a logarithmic singularity at the sonic throat and confirms the expected properties at the shock. 1.
An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method
, 2005
"... Professor Darmofal and the generous funding provided by NASA Langley (grant number NAG103035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higherorder DG. In particular, Krzysztof Fidkowsk ..."
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Cited by 29 (0 self)
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Professor Darmofal and the generous funding provided by NASA Langley (grant number NAG103035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higherorder DG. In particular, Krzysztof Fidkowski and Todd Oliver are to be acknowledged for their contributions towards the development of the flow solvers and also for providing some of the grids for the test cases demonstrated. Finally, thanks must go to thesis committee members Professors Peraire and Willcox as well as thesis readers Dr. Natalia Alexandrov and Dr. Steven Allmaras for the time they put into reading the thesis and providing the valuable feedbacks. 3 46 Adjoint approach to shape sensitivity 117 6.1 Introduction...............................
Multidisciplinary Design Optimization Techniques: Implications and Opportunities for Fluid Dynamics Research
 JAROSLAW SOBIESZCZANSKISOBIESKI AND RAPHAEL T. HAFTKA ”MULTIDISCIPLINARY AEROSPACE DESIGN OPTIMIZATION: SURVEY OF RECENT DEVELOPMENTS,” 34TH AIAA AEROSPACE SCIENCES MEETING AND EXHIBIT
, 1999
"... A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the de ..."
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Cited by 24 (0 self)
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A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.
Adjoint Error Correction for Integral Outputs
"... Introduction 1.1 Output functionals Why do engineers perform CFD calculations? In the case of a transport aircraft at cruise conditions, a calculation might be performed to investigate whether there is an adverse pressure gradient near the leading edge of the wing, causing boundary layer separatio ..."
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Cited by 21 (2 self)
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Introduction 1.1 Output functionals Why do engineers perform CFD calculations? In the case of a transport aircraft at cruise conditions, a calculation might be performed to investigate whether there is an adverse pressure gradient near the leading edge of the wing, causing boundary layer separation and premature transition. Alternatively, one might be concerned about wing/pylon/nacelle integration, in which case one might be looking to see if there are any shocks on the pylon, leading to unacceptable integration losses. In both of these examples, qualitative information is being obtained from the computed ow eld to understand and interpret the impact of the phenomena on the quantitative outputs of most concern to the aeronautical engineer, the lift and drag on the aircraft. The quality of the CFD calculation is judged, rst and foremost, by the accuracy of the lift and drag predictions. The details of the ow eld are much less important, and are used in a more qualitative manner t
A Survey Of Shape Parameterization Techniques
, 1999
"... This paper provides a survey of shape parameterization techniques for multidisciplinary ..."
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Cited by 16 (1 self)
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This paper provides a survey of shape parameterization techniques for multidisciplinary
Approach For Uncertainty Propagation And Robust Design In Cfd Using Sensitivity Derivatives
 Design in CFD Using Sensitivity Derivatives, AIAA Paper 20012528,inAIAA15 th Computational Fluid Dynamics Conference
, 2001
"... This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a first and secondorder statistical ..."
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Cited by 15 (2 self)
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This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a first and secondorder statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first and secondorder sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first order sensitivity derivatives appear in the objective function and system constraints. Secondorder sensitivity derivatives are used in a gradientbased search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values. Nomenclature A nozzle area a geometric shape parameter b geometric shape parameter b vector of independent input variables F vector of CFD output functions g vector of conventional optimization constraints k number of standard deviations M Mach number at nozzle inlet M vector of Mach number at each grid point _____________________________________ * LTC, US Army, Ph.D. Candidate, Department of Mechanical Engineering, mputko@tabdemo.larc.nasa.gov +Senior Research Scientist, Multidisciplinary Optimization Branch, M/S 159, p.a.newman@larc.nasa.gov # Associate Professor, Department of Mechanical Engineering, ataylor@lions.odu.edu Research Scienti...