Numerical Methods for Aerodynamic Shape Optimization

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances.When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics …


1 Introduction
1.1 A short history of aerodynamic design
1.1.1 Before modern aviation
1.1.2 Before modern computer
1.2 Design with Computational Fluid Dynamic
1.2.1 From inverse design to optimization
1.2.2 Adjoint equations in CFD
1.2.3 Automatic Differentiation
2 Summary of papers
2.1 Paper I
2.1.1 Discrete sensitivities
2.1.2 Edge-based finite-volume discretization
2.1.3 Optimization in 2D and 3D
2.2 Paper II
2.2.1 Disturbance energy and shape gradient
2.2.2 Parameterization
2.2.3 Results
2.3 Paper III
2.3.1 Geometrical interpolation
2.3.2 Performances
2.3.3 Gradient-based shape optimization
2.4 Paper IV
2.4.1 Moving mesh adaptation
2.4.2 A 2D inverse problem
2.4.3 Solution algorithm
3 Perspectives
3.1 From Euler to RANS
3.2 Error estimates in mesh adaptation
3.3 Interpolation of scattered data
3.4 Shape parameterization with constraints
4 Summary in Swedish

Author: Amoignon, Olivier

Source: Uppsala University Library

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