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27
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
Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation
, 1997
"... A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a secondorder accurate discretization method is described. The relationship between the continuous formulation and a discret ..."
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Cited by 101 (3 self)
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A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a secondorder accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finitedifference gradients and several design examples are presented.
Adjoint Recovery of Superconvergent Functionals from Approximate Solutions of Partial Differential Equations
, 1998
"... Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that ..."
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Cited by 55 (9 self)
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Abstract. Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasionedimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. Key words. PDEs, adjoint equations, error analysis, superconvergence AMS subject classifications. 65G99, 76N15 PII. S0036144598349423
FLOW CONTROL: New Challenges for a New Renaissance
 Progress in Aerospace Sciences 37
, 2001
"... this paper surveys a few recent attempts at bridging the gaps between the several scientific disciplines comprising the field of flow control, in an attempt to clarify the author's perspective on how recent advances in these constituent disciplines fit together in a manner that opens up significant ..."
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Cited by 21 (2 self)
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this paper surveys a few recent attempts at bridging the gaps between the several scientific disciplines comprising the field of flow control, in an attempt to clarify the author's perspective on how recent advances in these constituent disciplines fit together in a manner that opens up significant new research opportunities.
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 18 (8 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...
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.
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.
Airfoil Design by an AllAtOnce Method
, 1997
"... The allatonce approach is implemented to solve an optimum airfoil design problem. The airfoil design problem is formulated as a constrained optimization problem in which flow variables and design variables are viewed as independent and the coupling steady state Euler equation is included as a cons ..."
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Cited by 9 (0 self)
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The allatonce approach is implemented to solve an optimum airfoil design problem. The airfoil design problem is formulated as a constrained optimization problem in which flow variables and design variables are viewed as independent and the coupling steady state Euler equation is included as a constraint, along with geometry and other constraints. In this formulation, the optimizer computes a sequence of points which tend toward feasiblility and optimality at the same time (allatonce). This decoupling of variables typically makes the problem less nonlinear and can lead to more efficient solutions. In this paper an existing optimization algorithm is combined with an existing flow code. The problem formulation, its discretization, and the underlying solvers are described. Implementation issues are presented and numerical results are given which indicate that the cost of solving the design problem is approximately six times the cost of solving a single analysis problem.
A Coupled AeroStructural Optimization Method For Complete Aircraft Configurations
 AIAA 37th Aerospace Sciences Meeting
, 1999
"... This paper presents a new framework for the coupled optimization of aerostructural systems. The framework permits the use of highfidelity modeling of both the aerodynamics and the structures and represents our first step in an effort towards the development of a highfidelity multidisciplinary opt ..."
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Cited by 7 (4 self)
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This paper presents a new framework for the coupled optimization of aerostructural systems. The framework permits the use of highfidelity modeling of both the aerodynamics and the structures and represents our first step in an effort towards the development of a highfidelity multidisciplinary optimization capability. The approach is based on efficient analysis methodologies for the solution of the aerodynamics and structures subproblems, an adjoint solver to obtain aerodynamic sensitivities, and a multiprocessor parallel implementation. We have placed a geometry database representing the outer mold line (OML) of the configuration of interest at the core of our framework. Using this geometry description, the information exchange between aerodynamics and structures is accomplished through an independent coupling of each discipline with the OML database. The framework permits the later inclusion of other disciplines, such as heat transfer and radar signatures, with relative ease. Specific results from the coupling of a finite volume flow solver for the Euler and Reynolds Averaged NavierStokes # AIAA Member, Research Scientist, NASA Ames Research Center, MS 2276, Mo#ett Field, CA 94035, U.S.A. AIAA Member, Assistant Professor, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, U.S.A # AIAA Student Member, Graduate Student, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, U.S.A AIAA Member, Research Scientist, NASA Ames Research Center, MS 2276, Mo#ett Field, CA 94035, U.S.A. Copyright c #1999 by the American Institute of Aeronautics and Astronautics, Inc. No Copyright is asserted in the United States under Title 17, U.S. Code. The U. S. Government has a royaltyfree license to exercise all r...