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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 23 (6 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
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 20 (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.
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 17 (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.
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 15 (6 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.
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 14 (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
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 14 (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...............................
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 11 (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...
A Survey Of Shape Parameterization Techniques
, 1999
"... This paper provides a survey of shape parameterization techniques for multidisciplinary ..."
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Cited by 7 (1 self)
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This paper provides a survey of shape parameterization techniques for multidisciplinary
Analytic Adjoint Solutions for the Quasi1D Euler Equations
"... this paper we have undertaken a detailed investigation of adjoint solutions for the quasi1D Euler equations, focusing in particular on the solution behaviour at a shock or a sonic point where there is a change in sign of one of the hyperbolic characteristics. Formulating the adjoint equations using ..."
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Cited by 6 (1 self)
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this paper we have undertaken a detailed investigation of adjoint solutions for the quasi1D Euler equations, focusing in particular on the solution behaviour at a shock or a sonic point where there is a change in sign of one of the hyperbolic characteristics. Formulating the adjoint equations using Lagrange multipliers to enforce the RankineHugoniot shock jump conditions proves that, contrary to previous literature, the adjoint variables are continuous at the shock. This result is supported by the derivation of a closed form solution to the adjoint equations using a Green's function approach. In addition to proving the existence of a log(x) singularity at the sonic point, this closed form solution should be very helpful as a test case for others developing numerical methods for the adjoint equations. Future research will attempt to extend this analysis to two dimensions. Preliminary analysis, supported by the results of numerical computations (Giles & Pierce 1997), shows that the adjoint variables are again continuous at a shock, and that an adjoint boundary condition is required along the length of the shock. However, since adjoint computations currently employed for transonic aerofoil optimisation do not enforce this internal boundary condition, it remains an open question as to whether there is a consistency error in the limit of increasing grid resolution. In two dimensions, numerical evidence suggests that there is no longer a singularity at a sonic line if (as is usually the case) it is not orthogonal to the ow. This can be explained qualitatively by considering the region of inuence of points in the neighbourhood of the sonic line (Giles & Pierce 1997). An important new feature that must be considered for twodimensional ows is the behavior of the adjoint sol...