The Vertex Morphing method for node-based shape optimization

SUMMARY
One of the major challenges of shape optimisation in practical industrial cases is to generically parametrise the wide range of complex shapes. A novel approach is presented, which takes CAD descriptions as input and produces the optimal shape in CAD form using the control points of the Non-Uniform Rational B-Splines (NURBS) boundary representation as design variables. An implementation of the NURBS equations in source allows to include the CAD-based shape deformation inside the design loop and evaluate its sensitivities efficiently and robustly. In order to maintain or establish the required level of geometric continuity across patch interfaces, geometric constraints are imposed on the control point displacements. The paper discusses the discrete adjoint flow solver used and the computation of the complete sensitivities of the design loop by differentiating all components using automatic differentiation tools. The resulting rich but smooth deformation space is demonstrated on the optimisation of a vehicle climate duct. Copyright © 2013 John Wiley & Sons, Ltd.

CAD‐based shape optimisation with CFD using a discrete adjoint

Stabilisation of discrete steady adjoint solvers

An approach is presented for determining which parameters defining the features in a CAD model need to be modified, and by what amount, to optimize component performance. It uses sensitivities computed for the parameters to determine the change required in each to optimize the component. Parametric sensitivity is computed by combining a measure of boundary movement due to a parameter perturbation, known as design velocity, and an adjoint sensitivity map over the boundary. The sensitivity map results from an adjoint analysis and approximates the change in objective function (performance) due to a movement of the boundary. Gradient based optimization is used based on the parametric sensitivities.This presented method is significantly less computationally expensive than alternative approaches, and has the advantage that optimization is based on the parameters defining the CAD model, allowing it to be integrated into design workflows. The efficiency of the approach allows all of the parameters in the ...

/pdf/optimizing-parameterized-cad-geometries-using-sensitivities-29g61b4mah.pdf

Optimizing parameterized CAD geometries using sensitivities based on adjoint functions

Ag eneral and unif ied geometry framework based on non-uniform rational B-splines is presented. One key aspect of this framework is the use of free-form deformation where the control points defining the geometry itself are embedded rather than the usual surface grid points. This ensures that one maintains an analytical representation of the geometry as it deforms and, if required, also enables the use of an integrated algorithm for mesh movement. The flexibility and robustness of the proposed approach are demonstrated in the context of aerodynamic shape optimization by maximizing, using an Euler-based flow solver and gradient-based optimizer, the lift-to-drag ratio of an initially half-sphere-shaped geometry. Sensitivities are computed analytically via the discrete adjoint method.

http://oddjob.utias.utoronto.ca/dwz/Miscellaneous/Gagnon_Zingg_MAO_2012.pdf

Two-Level Free-Form Deformation for High-Fidelity Aerodynamic Shape Optimization

CAD-based shape optimisation using adjoint sensitivities

Preparation and assembly of discrete adjoint CFD codes

Pseudo-timestepping and verification for automatic differentiation derived CFD codes

This paper presents some insights into constructing sensitivity algorithms, the tools required, what the constraints are and how to assemble the program. In this work Tapenade (2), a source transformation automatic dierentiation tool, is used to obtain the sensitivity of a CFD system, whereby the independent and dependent variables are user- dened. Points on how to prepare the source code are detailed, with the aim of enabling the programmer to submit safe transformable code to Tapenade whilst retaining the use of modern Fortran structures, making use of modules, derived data types, pointers, etc.

Faidon Christakopoulos

Papers

CAD-based shape optimisation using adjoint sensitivities

Preparation and assembly of discrete adjoint CFD codes

Pseudo-timestepping and verification for automatic differentiation derived CFD codes

Adjoint cfd codes through automatic differentiation