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Recent Improvements in Aerodynamic Design Optimization On Unstructured Meshes
 AIAA JOURNAL
, 2002
"... Recent improvements in an unstructuredgrid method for largescale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, par ..."
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Recent improvements in an unstructuredgrid method for largescale aerodynamic design are presented. Previous work had shown such computations to be prohibitively long in a sequential processing environment. Also, robust adjoint solutions and mesh movement procedures were difficult to realize, particularly for viscous flows. To overcome these limiting factors, a set of design codes based on a discrete adjoint method is extended to a multiprocessor environment using a shared memory approach. A nearly linear speedup is demonstrated, and the consistency of the linearizations is shown to remain valid. The full linearization of the residual is used to precondition the adjoint system, and a significantly improved convergence rate is obtained. A new mesh movement algorithm is implemented and several advantages over an existing technique are presented. Several design cases are shown for turbulent flows in two and three dimensions.
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 15 (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
Aerodynamic Design on Unstructured Grids for Turbulent Flows
 NASA TM
, 1997
"... An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables to obtain derivatives of the cost function. The solution of the adjoint equations is obtained by using an implicit formulation in which the turbulence mo ..."
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Cited by 15 (4 self)
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An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables to obtain derivatives of the cost function. The solution of the adjoint equations is obtained by using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finitedifference gradients and a few sample computations are shown. In addition, a user interface is described that significantly reduces the time required to set up the design problems. Recommendations on directions of further research into the NavierStokes design process are made.
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...............................
Aerodynamic Design Sensitivities on an Unstructured Mesh Using the NavierStokes Equations and a Discrete Adjoint Formulation
, 1998
"... A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the threedimensional Reynoldsaveraged NavierStokes equations coupled with a oneequation turbulence model. A discussion of the numerical implementation of ..."
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Cited by 10 (3 self)
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A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the threedimensional Reynoldsaveraged NavierStokes equations coupled with a oneequation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complexvariable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A firstorder approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a “frozen ” eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partiallyconverged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
 Computers & Fluids
, 2003
"... this report is for accurate reporting and does not constitute an official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration ..."
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this report is for accurate reporting and does not constitute an official endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration
Implementation of a Parallel Framework for Aerodynamic Design Optimization on Unstructured Meshes
"... A parallel framework for performing aerodynamic design optimizations on unstructured meshes is described. The approach utilizes a discrete adjoint formulation which has previously been implemented in a sequential environment and is based on the threedimensional Reynoldsaveraged NavierStokes eq ..."
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Cited by 1 (0 self)
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A parallel framework for performing aerodynamic design optimizations on unstructured meshes is described. The approach utilizes a discrete adjoint formulation which has previously been implemented in a sequential environment and is based on the threedimensional Reynoldsaveraged NavierStokes equations coupled with a oneequation turbulence model. Here, only the inviscid terms are treated in order to develop a basic foundation for a multiprocessor design methodology. A parallel version of the adjoint solver is developed using a library of MPIbased linear and nonlinear solvers known as PETSc, while a sharedmemory approach is taken for the mesh movement and gradient evaluation codes. Parallel efficiencies are demonstrated and the linearization of the residual is shown to remain valid.