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36
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 106 (45 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
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...
Aerodynamic Shape Optimization Techniques Based On Control Theory
 Control Theory, CIME (International Mathematical Summer
, 1998
"... This paper review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow . The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acti ..."
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Cited by 30 (25 self)
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This paper review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow . The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wingbody combinations and inviscid optimization of complex configurations.
High performance supersonic missile inlet design using automated optimization
 In AIAA Symposium on Multidisciplinary Analysis and Optimization '96
, 1996
"... A multilevel design strategy for supersonic missile inlet design is developed. The multilevel design strategy combines an ef � cient simple physical model analysis tool and a sophisticated computational � uid dynamics (CFD) Navier – Stokes analysis tool. The ef � cient simple analysis tool is incorp ..."
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Cited by 14 (13 self)
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A multilevel design strategy for supersonic missile inlet design is developed. The multilevel design strategy combines an ef � cient simple physical model analysis tool and a sophisticated computational � uid dynamics (CFD) Navier – Stokes analysis tool. The ef � cient simple analysis tool is incorporated into the optimization loop, and the sophisticated CFD analysis tool is used to verify, select, and � lter the � nal design. The genetic algorithms and multistart gradient line search optimizers are used to search the nonsmooth design space. A geometry model for the supersonic missile inlet is developed. A supersonic missile inlet that starts at Mach 2.6 and cruises at Mach 4 was designed. Signi � cant improvement of the inlet total pressure recovery has been obtained. Detailed � ow � eld analysis is also presented. I.
A Comparison of the Continuous and Discrete Adjoint Approach to Automatic Aerodynamic Optimization
, 2000
"... This paper compares the continuous and discrete adj intbased automatic aerodynamic optimization. The obj ective is to study the tradeo# between the complexity of the discretization of the adj int equation for both the continuous and discrete approach, the accuracy of the resulting estimate of th ..."
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Cited by 14 (4 self)
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This paper compares the continuous and discrete adj intbased automatic aerodynamic optimization. The obj ective is to study the tradeo# between the complexity of the discretization of the adj int equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this paper presents complete formulations and discretization of the Euler equations, the continuous adj int equation and its counterpart the discrete adj oint equation. The di#erences between the continuous and discrete boundary conditions are also explored. Second, the results demonstrate twodimensional inverse pressure design and drag minimization problems as well as the accuracy of the sensitivity derivatives obtained from continuous and discrete adj ointbased equations compared to finitedi#erence gradients.
Computational Fluid Dynamics for Aerodynamic Design: Its . . .
 Its Current and Future Impact, AIAA 20010538, 39th AIAA Aerospace Sciences Meeting & Exhibit
, 2001
"... This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disc ..."
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Cited by 13 (7 self)
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This paper discusses the role that computational fluid dynamics plays in the design of aircraft. An overview of the design process is provided, covering some of the typical decisions that a design team addresses within a multidisciplinary environment. On a very regular basis tradeoffs between disciplines have to be made where a set of conflicting requirements exist. Within an aircraft development project, we focus on the aerodynamic design problem and review how this process has been advanced, first with the improving capabilities of traditional computational fluid dynamics analyses, and then with aerodynamic optimizations based on these increasingly accurate methods. The optimization method of the present work is based on the use of the adjoint of the flow equations to compute the gradient of the cost function. Then, we use this gradient to navigate the design space in an efficient manner to find a local minimum. The computational costs of the present method are compared with that of other approaches to aerodynamic optimization. A brief discussion regarding the formulation of a continuous adjoint, as opposed to a discrete one, is also included. Two case studies are provided...
Aerodynamic Shape Optimization Using the Adjoint Method
 VKI Lecture Series on Aerodynamic Drag Prediction and Reduction, von Karman Institute of Fluid Dynamics, Rhode St Genese
, 2003
"... These Lecture Notes review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary sh ..."
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Cited by 13 (9 self)
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These Lecture Notes review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wingbody combinations.
Studies Of The Continuous And Discrete Adjoint Approaches To Viscous Automatic Aerodynamic Shape Optimization
, 2001
"... This paper compares the continuous and discrete viscous adj ointbased automatic aerodynamic optimization. The obj1GMI e is to study the complexity of the discretization of the adj int equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, a ..."
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Cited by 12 (4 self)
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This paper compares the continuous and discrete viscous adj ointbased automatic aerodynamic optimization. The obj1GMI e is to study the complexity of the discretization of the adj int equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this paper presents complete formulations and discretizations of the NavierStokes equations, the continuous viscous adj oint equation and its counterpart the discrete viscous adj oint equation. The di#erences between the continuous and discrete boundary conditions are also explored. Second, the accuracy of the sensitivity derivatives obtained from continuous and discrete adj ointbased equations are compared to complexstep gradients. Third, the adj oint equations and its corresponding boundary conditions are formulated to quantify the influence of geometry modifications on the pressure distribution at an arbitrary remote location within the domain of interest. Finally, applications are presented for inverse, pressure and skin friction drag minimization, and sonic boom minimization problems.
Automatic Aerodynamic Optimization on Distributed Memory Architectures
 AIAA Paper
, 1996
"... This paper presents a parallel implementation of an automat Euler design method based on the control theory of systems governed by partial differential equations. The Euler equations and the resulting adjoint equations necessary to calculate the Frechet derivatives for t e gradient of the cost funct ..."
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Cited by 12 (6 self)
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This paper presents a parallel implementation of an automat Euler design method based on the control theory of systems governed by partial differential equations. The Euler equations and the resulting adjoint equations necessary to calculate the Frechet derivatives for t e gradient of the cost funct2 are solved using a domain decomposit approach with communication handled by the MPI (Message Passing Interface) Standard. Parallel performance is evaluated on a distributed memory parallel computer and sample calculations are presented. A complete optimization procedure on a 1923248 mesh can be completed in 7 minutes using 16 processors of an IBM SP2 system. This clearly shows that parallel processing is a key enabling technology for CFD to become an efficient tool in a realists design environment. The parallel implementation of a mult2 lock version of the program which allows for a higher degree of geometric complexity in the design has recently been completed. Parallel performance trends of the multiblock code are consistent with the ones observed in the single block implementation.