Adjoint code developments using the exact discrete approach

Giles, Michael B.; Duta, Mihai C.; Miiller, Jens-Dominik

doi:10.2514/6.2001-2596

Cited by 38 publications

(34 citation statements)

References 24 publications

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“…The memory requirements and CPU cost per iteration for the adjoint harmonic code are only slightly larger than those for the linear harmonic code; the increase is associated with a marginally larger cost of evaluating the adjoint uxes [14]. However, the cost of the adjoint solution is practically identical with that of the linear solution for any application.…”

Section: Adjoint Harmonic Analysismentioning

confidence: 78%

“…The linear harmonic code has itself been validated at a subroutine level by comparison with the subroutines in the non-linear code [15,14]. In addition it has been checked using a range of testcases, starting with simple model problems such as inviscid ow over 2D at plate cascades for which there is an analytic solution [16].…”

Section: Validationmentioning

confidence: 99%

“…For the harmonic adjoint code, the validation has been performed at two levels. At the lower level, each subroutine has been checked for consistency with its counterpart in the linear harmonic code [15,14]. At the higher level, it has been checked that the adjoint and linear harmonic codes produce the same value for the worksum output, to within machine accuracy, at each step of the iterative process.…”

Section: Validationmentioning

confidence: 99%

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The harmonic adjoint approach to unsteady turbomachinery design

Duta

Giles

Campobasso

2002

Numerical Methods in Fluids

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SUMMARYIn recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint ow analysis to e ciently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic ow unsteadiness.The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes.

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Section: Adjoint Harmonic Analysismentioning

confidence: 78%

Section: Validationmentioning

confidence: 99%

Section: Validationmentioning

confidence: 99%

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The harmonic adjoint approach to unsteady turbomachinery design

Duta

Giles

Campobasso

2002

Numerical Methods in Fluids

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“…Nielsen et al [20] extended the exact dual scheme for implicit solution algorithms and showed asymptotically equivalent convergence rates for the primal and dual systems. An exact dual algorithm of the improved SGS scheme based on References [16,19,20] is presented here. By writing…”

Section: Solution Algorithmmentioning

confidence: 99%

“…An improved version of SGS suggested by Whitfield [36] is implemented for the direct formulation. Recently, Giles et al [16,19] proposed an exact dual approach for solving the adjoint system to achieve exact numerical equivalence between the direct and adjoint discretizations. Nielsen et al [20] extended the exact dual scheme for implicit solution algorithms and showed asymptotically equivalent convergence rates for the primal and dual systems.…”

Section: Introductionmentioning

confidence: 99%

Discrete direct and adjoint sensitivity analysis for arbitrary Mach number flows

Balasubramanian

Newman

2006

Int. J. Numer. Meth. Engng

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SUMMARYParallel discrete direct and adjoint sensitivity analysis capabilities are developed for arbitrary Mach flows on mixed-element unstructured grids. The discrete direct and adjoint methods need a consistent and complete linearization of the flow-solver to obtain accurate derivatives. The discontinuous nature of the commonly used unstructured flux-limiters, like Barth-Jespersen and Venkatakrishnan, make them unsuitable for sensitivity analysis. A modification is proposed to make these limiters piecewise continuous and numerically differentiable, without compromising the monotonicity conditions. An improved version of Symmetric Gauss-Seidel that significantly reduces the computational cost is implemented. A distributed-memory message passing model is employed for the parallelization of sensitivity analysis solver. These algorithms are implemented within a three-dimensional unstructured grid framework and results are presented for inviscid, laminar and turbulent flows.

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Formulation and Multigrid Solution of the Discrete Adjoint Problem on Unstructured Meshes

Mavriplis

Computational Fluid Dynamics 2004

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Adjoint code developments using the exact discrete approach

Cited by 38 publications

References 24 publications

The harmonic adjoint approach to unsteady turbomachinery design

The harmonic adjoint approach to unsteady turbomachinery design

Discrete direct and adjoint sensitivity analysis for arbitrary Mach number flows

Formulation and Multigrid Solution of the Discrete Adjoint Problem on Unstructured Meshes

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