Optimal Design and Computational Fluid Dynamics

The course is devoted to the presentation and the practical application of a panel of numerical techniques currently used by the engineer to perform the optimal design of fluidic devices (shape optimization, optimal choice of design parameters of geometrical or other nature). The course displays two key original features:

• the described techniques are systematically linked with the CFD tools available for the engineer, with a distinction between open-source (modifiable) tools and close (commercial) codes.
• the presentation progresses from problems where a large quantity of information is available for the design (numerous values of objective functions and gradients) to problems where only a very limited amount of information is available (few values of the objective functions).

1. Gradient-based optimization in CFD. Finite-difference estimate and adjoint approach. Extension to multi-objective problems. BE#1 & #2 : solution of model and engineering problems.
2. Gradient-free optimization. From direct search to metaheuristics. Ideal multi-objective optimization. BE#3, #4 &#5 : solution of model and engineering problems (heat exchanger, wind farm); start of the project.
3. Derivation of surrogate models for high-cost objectives. BE#6, #7 : solution of a shape optimization or a power maximization problem.
4. Key concepts of robust optimization. Uncertainty quantification and propagation (Polynomial Chaos). BE #8 : robust optimization of a previously solved problem.