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25
Optimum aerodynamic design using the NavierStokes equations
 Theoretical and Computational Fluid Dynamics
, 1998
"... The ultimate success of an aircraft design depends on the resolution of complex multidisciplinary tradeo s between factors such as aerodynamic eciency, structural weight, stability and control, and ..."
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Cited by 121 (46 self)
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The ultimate success of an aircraft design depends on the resolution of complex multidisciplinary tradeo s between factors such as aerodynamic eciency, structural weight, stability and control, and
PROBLEM FORMULATION FOR MULTIDISCIPLINARY OPTIMIZATION
, 1994
"... This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization. The paper has three goals. First, it is an expository introduction to MDO aimed at those who do research on optimization algorithms, since the optimizati ..."
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Cited by 91 (8 self)
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This paper is about multidisciplinary (design) optimization, or MDO, the coupling of two or more analysis disciplines with numerical optimization. The paper has three goals. First, it is an expository introduction to MDO aimed at those who do research on optimization algorithms, since the optimization community has much to contribute to this important class of computational engineering problems. Second, this paper presents to the MDO research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems. Third, the "individual discipline feasible " (IDF) approaches introduced here make use of existing specialized analysis codes, and they introduce significant opportunities for coarsegrained computational parallelism particularly well suited to heterogeneous computing environments. The key distinguishing characteristic of the three fundamental approaches to MDO formulation discussed here is the kind of disciplinary feasibility that must be maintained at each optimization iteration. Other formulation issues, such as the sensitivities required, are also considered. This discussion highlights the tradeoffs between reuse of existing software, computational requirements, and probability of success.
Adjoint equations in CFD: duality, boundary conditions and solution behaviour
, 1997
"... The first half of this paper derives the adjoint equations for inviscid and viscous compressible flow, with the emphasis being on the correct formulation of the adjoint boundary conditions and restrictions on the permissible choice of operators in the linearised functional. It is also shown that the ..."
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Cited by 30 (12 self)
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The first half of this paper derives the adjoint equations for inviscid and viscous compressible flow, with the emphasis being on the correct formulation of the adjoint boundary conditions and restrictions on the permissible choice of operators in the linearised functional. It is also shown that the boundary conditions for the adjoint problem can be simplified through the use of a linearised perturbation to generalised coordinates. The second half of the paper constructs the Green's functions for the quasi1D and 2D Euler equations. These are used to show that the adjoint variables have a logarithmic singularity at the sonic line in the quasi1D case, and a weak inverse squareroot singularity at the upstream stagnation streamline in the 2D case, but are continuous at shocks in both cases. 1 Introduction The last few years have seen considerable progress in the use of adjoint equations in CFD for optimal design [19]. In all of the methods, the heart of the algorithm is an optimisati...
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 25 (7 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
Contribution to the Optimal Shape Design of TwoDimensional Internal Flows with Embedded Shocks
, 1995
"... We explore the praticability of optimal shape design for ows modeled by the Euler equations. We de ne a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solvi ..."
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Cited by 24 (4 self)
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We explore the praticability of optimal shape design for ows modeled by the Euler equations. We de ne a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a costate equation. The optimization problem is then examined by comparing the performance of several gradientbased optimization algorithms. In this formulation, the ow eld can be computed to an arbitrary order of accuracy. Finally, some results for internal ows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.
Control theory based airfoil design using the Euler equations
 AIAA paper 944272, 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City Beach, FL
, 1994
"... This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies [6, 71 it was shown that control theory could be used to devise an effective optimization procedure for twodimensional profiles in which the shape is determined by a co ..."
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Cited by 23 (6 self)
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This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies [6, 71 it was shown that control theory could be used to devise an effective optimization procedure for twodimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat threedimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions. Nomenclature A,, grid transformation coefficients b design variable B generic costate variable c speed of sound C bounding surface of flowfield domain on airfoil Cd coefficient of drag Ci coefficient of lift C, coefficient of pressure
Automatic Differentiation Of Advanced CFD Codes For Multidisciplinary Design
 Journal on Computing Systems in Engineering
, 1992
"... This paper addresses one such synergism for computa ..."
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Cited by 23 (16 self)
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This paper addresses one such synergism for computa
On the Properties of Solutions of the Adjoint Euler Equations
 Numerical Methods for Fluid Dynamics VI. ICFD
, 1998
"... The behavior of analytic and numerical adjoint solutions is examined for the quasi1D 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 ..."
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Cited by 21 (9 self)
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The behavior of analytic and numerical adjoint solutions is examined for the quasi1D 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 isentropic and shocked transonic flow, revealing a logarithmic singularity at the sonic throat and confirming the expected properties at the shock. Numerical solutions obtained using both discrete and continuous adjoint formulations reveal that there is no need to explicitly enforce the adjoint shock boundary condition. Adjoint methods are demonstrated to play an important role in the error estimation of integrated quantities such as lift and drag. 1 Introduction Adjoint problems arise naturally in the formulation of methods for optimal aerodynamic design and optimal error control. F...
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 17 (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