Applied Computational Fluid Dynamics Techniques: An Introduction Based on Finite Element Methods, 2nd Edition

20 OPTIMAL SHAPE AND PROCESS DESIGN

The ability to compute flowfields implicitly implies the ability to optimize shapes and processes. The change of shape in order to obtain a desired or optimal performance is denoted as optimal shape design. Due to its immense industrial relevance, the relative maturity (accuracy, speed) of flow solvers and increasingly powerful computers, optimal shape design has elicited a large body of research and development (Newman et al. (1999), Mohammadi and Pironneau (2001)). The present chapter gives an introduction to the key ideas, as well as the optimal techniques to optimize shapes and processes.

20.1. The general optimization problem

In order to optimize a process or shape, a measurement of quality is required. This is given by one – or possibly many – so-called objective functions I, which are functions of design variables or input parameters β, as well as field unknowns u (e.g. a flowfield)

and is subject to a number of constraints.

• PDE constraints: these are the equations that describe the physics of the problem being considered, and may be written as

  

• Geometric constraints:

  

• Physical constraints:

Examples for objective functions are: