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25
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.
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 21 (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
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.
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.
Adjoint Code Developments Using the Exact Discrete Approach
 AIAA PAPER
, 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. With a new iterative procedure for solving the adjoint equations, exact n ..."
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Cited by 10 (4 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. With a new iterative procedure for solving the adjoint equations, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady flow in turbomachinery
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 7 (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...
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...
The Harmonic Adjoint Approach to Unsteady Turbomachinery Design
 ICFD Conference
, 2001
"... This paper demonstrates how the worksum output produced by the linear harmonic ow analysis can be obtained by an adjoint harmonic analysis which, under certain conditions, is a more ecient alternative to the usual linear approach. The adjoint approach has been developed for aeronautical optimal desi ..."
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Cited by 6 (2 self)
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This paper demonstrates how the worksum output produced by the linear harmonic ow analysis can be obtained by an adjoint harmonic analysis which, under certain conditions, is a more ecient alternative to the usual linear approach. The adjoint approach has been developed for aeronautical optimal design by Jameson [10, 11]. At each optimisation step, a single adjoint ow calculation determines the sensitivity of a steadystate functional (e.g. lift or drag) to a large number of geometric design parameters. The same idea is applied in this paper in the context of linear unsteady ow analysis, to compute the worksum values corresponding to any input unsteady ow perturbations, whereas the usual approach would require a separate linear unsteady ow calculation for each set of inputs
Improving the Aircraft Design Process Using Webbased Modeling and Simulation
 ACM Transactions on Modeling and Computer Simulation
, 2000
"... n of simulation models, distributed heterogeneous execution, and dynamic multimedia documentation, has the potential to meet these requirements. This paper outlines the current aircraft design process, highlighting its problems and complexities, and presents our vision of an aircraft design process ..."
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Cited by 5 (0 self)
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n of simulation models, distributed heterogeneous execution, and dynamic multimedia documentation, has the potential to meet these requirements. This paper outlines the current aircraft design process, highlighting its problems and complexities, and presents our vision of an aircraft design process using Webbased modeling and simulation. Categories and Subject Descriptors: I.6.5 [Simulation Modeling]: Model Developmentmodeling methodologies; I.6.8 [Simulation Modeling]: Types of Simulationdistributed General Terms: Design Additional Key Words and Phrases: Webbased simulation, aircraft design, Java, objectoriented 1. INTRODUCTION Intensive competition in the commercial aviation industry is placing increasing pressure on aircraft manufacturers to reduce the time, cost and risk of product development. To compete effectively in today's global marketplace, innovative approaches to reducing