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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 108 (4 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.
Grid adaptation for functional outputs: application to twodimensional inviscid flows
 J. Comput. Phys
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Preconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes
 J. Comput. Phys
, 1997
"... this paper are not intended for preconditioning in the limit of incompressibility. For typical viscous meshes, the Mach number remains sufficiently large, even in the cells near the wall, that the tip of the vorticity footprint remains distinguishable from the origin as in Fig. 7a. For most boundary ..."
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Cited by 24 (7 self)
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this paper are not intended for preconditioning in the limit of incompressibility. For typical viscous meshes, the Mach number remains sufficiently large, even in the cells near the wall, that the tip of the vorticity footprint remains distinguishable from the origin as in Fig. 7a. For most boundary layer cells, the Mach number is large enough that even the vorticity footprint is clustered well away from the origin as in Fig. 8a. The interaction between the preconditioner and multigrid algorithm is critical, since the preconditioner is chiefly responsible for damping the convective modes and the coarsening strategy is essential to damping the acoustic modes.
A new high resolution scheme for compressible viscous ows with shocks
 AIAA paper To Appear, AIAA 33nd Aerospace Sciences Meeting
, 1995
"... A new flux splitting and limiting technique which yields onepoint stationary shock capturing is presented. The technique is applied to the full NavierStokes and Reynolds Averaged NavierStokes equations. Calculations of laminar boundary layers at subsonic and supersonic speeds are presented togeth ..."
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Cited by 17 (12 self)
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A new flux splitting and limiting technique which yields onepoint stationary shock capturing is presented. The technique is applied to the full NavierStokes and Reynolds Averaged NavierStokes equations. Calculations of laminar boundary layers at subsonic and supersonic speeds are presented together with calculations of transonic flows around airfoils. The results exhibit very good agreement with theoretical solutions and existing experimental data. It is found that. the proposed scheme improves the resolution of viscous flows while maintaining excellent onepoint shock capturing characteristics. 1
Accelerating ThreeDimensional NavierStokes Calculations
, 1997
"... This paper addresses the widely observed breakdown in multigrid performance for turbulent ..."
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Cited by 12 (3 self)
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This paper addresses the widely observed breakdown in multigrid performance for turbulent
Edgebased Multigrid and Preconditioning for Hybrid Grids
 AIAA Paper
, 1999
"... this paper is the extension of the edgecollapsing idea to hybrid grids. This proved to be more difficult than initially expected. Ideally, what one would like is a collapsing technique which preserves as much as possible of the structure within the grid. For example, if the fine grid consists of pr ..."
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Cited by 11 (10 self)
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this paper is the extension of the edgecollapsing idea to hybrid grids. This proved to be more difficult than initially expected. Ideally, what one would like is a collapsing technique which preserves as much as possible of the structure within the grid. For example, if the fine grid consists of prisms in the boundary layer, then one would ideally like the first coarse grid to consist of semicoarsened prisms in the boundary layer. However, Crumpton's edgecollapsing algorithm works by collapsing an edge, combining its two nodes into one, and connecting the new node to the faces of the cavity formed by the removal of the edge and all associated cells. When starting from a prismatic grid, this quickly results in a grid consisting solely of tetrahedra. Even worse, with a hexahedral grid it can result in a coarse grid which has fewer nodes, but an increased number of cells, many of which are tetrahedra.
An Unstructured Algorithm for High Reynolds Number Flows on HighlyStretched Grids
, 1998
"... This paper describes a robust and efficient algorithm for the numerical solution of the steady compressible Reynoldsaveraged NavierStokes equations, with a one equation turbulence model. Highly stretched triangular and tetrahedral unstructured grids are used to integrate the equations to the wall. ..."
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Cited by 7 (3 self)
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This paper describes a robust and efficient algorithm for the numerical solution of the steady compressible Reynoldsaveraged NavierStokes equations, with a one equation turbulence model. Highly stretched triangular and tetrahedral unstructured grids are used to integrate the equations to the wall. An edgecollapse multigrid approach is introduced which is shown to be efficient, robust and applicable to complex geometries in two and three dimensions, for inviscid and viscous flows. Special attention is paid to the treatment of the highly stretched grids in both the discretization and the edgecollapse multigrid method. 1 SPATIAL DISCRETIZATION This paper is concerned with solving the steady compressible Reynoldsaveraged NavierStokes equations in conjunction with the Spalart Allmaras turbulence model [1]. Collectively, these may be expressed as @ @x i F(e i ; Q;rQ) = S(Q;rQ): (1) Here Q(x) is the vector of conserved variables, (ae; aeu; aev; aew; E; ~ ) T , where ae is the dens...
On Some Numerical Dissipation Schemes
 Journal of Computational Physics
, 1998
"... Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete ..."
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Cited by 6 (0 self)
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Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finitevolume discretization and a multistage timestepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarsegrid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the sche...
FINITE ELEMENT CFD ANALYSIS OF SUPERMANEUVERING AND SPINNING STRUCTURES
"... This dissertation presents a spacetime finite element method for solving the compressible Euler equations in a noninertial reference frame. The methodology developed here has been formulated with an emphasis on solving problems that are found in aerospace applications. In particular, we are intere ..."
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Cited by 3 (0 self)
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This dissertation presents a spacetime finite element method for solving the compressible Euler equations in a noninertial reference frame. The methodology developed here has been formulated with an emphasis on solving problems that are found in aerospace applications. In particular, we are interested in modeling aeroservoelastic interactions for complicated threedimensional problems such as fighter aircraft. In this Chapter we discuss the background behind our current interest in the modeling of aeroservoelastic problems. This includes a discussion on the computational tools we seek to enhance through the development of a noninertial finite element methodology. We then proceed by defining the objectives of this research effort, and finish the introduction with a brief overview for the remaining Chapters of this document. 1.1 Background Modern highperformance aerospace vehicles are highly maneuverable, operate over a wide range of speeds, in some cases hypersonic speeds, and are designed to have lightweight, sometimes flexible structures. Examples of such vehicles currently being developed include the X33 single stage to orbit vehicle, the X43 or HyperX, and the X34 reusable launch vehicle technology demonstrator. Unfortunately, this type of vehicle often encounters aeroservoelastic (ASE) instabilities during part of its flight profile as a result of complicated aerodynamic, elastic, inertial, and control interactions. Hence, the accurate prediction of such interactions prior to flight testing is a necessary part of the design process. In terms of accuracy, the most attractive model for the aerodynamic interaction in an ASE analysis is a computational fluid dynamics (CFD) model. Unsteady CFD solutions provide an accurate physical model of the flow field for all ...
Assessment of the Simultaneous Perturbation Stochastic Approximation Method for Wing Design Optimization Problem
 Journal of Aircraft
"... Aerodynamic shape design optimization problems, such as inverse and constrained airfoil design and axisymmetric nozzle design, are investigated by applying the simultaneous perturbation stochastic approximation (SPSA) method to objective functions that are estimated during each design iteration usin ..."
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Cited by 3 (1 self)
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Aerodynamic shape design optimization problems, such as inverse and constrained airfoil design and axisymmetric nozzle design, are investigated by applying the simultaneous perturbation stochastic approximation (SPSA) method to objective functions that are estimated during each design iteration using a finite volume computational fluid dynamics technique for solving the compressible Navier–Stokes equations. The SPSA method has been demonstrated in the literature as having significant advantages over stochastic global optimization methods such as the simulated annealing (SA) method. In this work the SPSA is compared with SA method for a class of twodimensional and axisymmetric aerodynamic design optimization problems. The numerical studies show that the SPSA method is robust in reaching optimal aerodynamic shapes, is easy to implement, and is highly efficient. The SPSA method can also decrease the computational costs significantly compared with the SA method.