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16
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
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
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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Cited by 9 (4 self)
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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
Three–Dimensional Turbulent RANS Adjoint–Based Error Correction
 AIAA Paper
, 2003
"... Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predi ..."
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Cited by 8 (0 self)
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Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjointbased error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a userspecified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
AdjointBased, ThreeDimensional Error Prediction and Grid Adaptation
 AIAA Paper
, 2002
"... Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can o#er the possibility to minimize ..."
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Cited by 6 (2 self)
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Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can o#er the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust meshadaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for threedimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wingbody, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.
Adjoint Formulation for an EmbeddedBoundary Cartesian Method
, 2005
"... A discreteadjoint formulation is presented for the threedimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flowsensitivity equations leverages the Runge–Kutta timemarching scheme in conjunction with the parallel multig ..."
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Cited by 6 (2 self)
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A discreteadjoint formulation is presented for the threedimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flowsensitivity equations leverages the Runge–Kutta timemarching scheme in conjunction with the parallel multigrid method of the flow solver. The matrixvector products associated with the linearization of the flow equations are computed onthefly, thereby minimizing the memory requirements of the algorithm at a computational cost roughly equivalent to a flow solution. Threedimensional test cases, including a wingbody geometry at transonic flow conditions and an entry vehicle at supersonic flow conditions, are presented. These cases verify the accuracy of the linearization and demonstrate the efficiency and robustness of the adjoint algorithm for complexgeometry problems.
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
Aerodynamic Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
"... We present a new approach for the computation of shape sensitivities using the discrete adjoint and flowsensitivity methods on Cartesian meshes with general polyhedral cells (cutcells) at the wall boundaries. By directly linearizing the cutcell geometric constructors of the mesh generator, an effi ..."
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Cited by 4 (1 self)
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We present a new approach for the computation of shape sensitivities using the discrete adjoint and flowsensitivity methods on Cartesian meshes with general polyhedral cells (cutcells) at the wall boundaries. By directly linearizing the cutcell geometric constructors of the mesh generator, an efficient and robust computation of shape sensitivities is achieved. We show that the error convergence rate of the flow solution and its sensitivity, as well as the objective function and its gradient is consistent with the secondorder spatial discretization of the threedimensional Euler equations. The performance of the approach is demonstrated for an airfoil optimization problem in transonic flow, and a CADbased shape optimization of a reentry capsule in hypersonic flow. The approach is wellsuited for conceptual design studies where fast turnaround time is required. I.
On the Iterative Solution of Adjoint Equations
, 2000
"... This paper considers the iterative solution of the adjoint equations which arise in the context of design optimisation. It is shown that naive adjoining of the iterative solution of the original linearised equations results in an adjoint code which cannot be interpreted as an iterative solution of t ..."
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Cited by 4 (1 self)
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This paper considers the iterative solution of the adjoint equations which arise in the context of design optimisation. It is shown that naive adjoining of the iterative solution of the original linearised equations results in an adjoint code which cannot be interpreted as an iterative solution of the adjoint equations. However, this can be achieved through appropriate algebraic manipulations. This is important in design optimisation because one can reduce the computational cost by starting the adjoint iteration from the adjoint solution obtained in the previous design step.