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**Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation.**
*(English)*
Zbl 0968.76074

Summary: We develop and analyze a continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids. The derivation of the co-state equations is presented, and a second-order accurate discretization method is described. We explore the relationship between the continuous formulation and a discrete formulation 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. Finally, we describe a method 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 finite-difference gradients and several design examples.

### MSC:

76N25 | Flow control and optimization for compressible fluids and gas dynamics |

76D55 | Flow control and optimization for incompressible viscous fluids |

76M12 | Finite volume methods applied to problems in fluid mechanics |

### Keywords:

design optimization; continuous adjoint formulation; inviscid flows; sensitivity derivatives; unstructured grids; co-state equations; second-order accurate discretization; viscous flow### Software:

ADIFOR
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\textit{W. K. Anderson} and \textit{V. Venkatakrishnan}, Comput. Fluids 28, No. 4--5, 443--480 (1999; Zbl 0968.76074)

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### References:

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