Introduction

Industrial design tends to be multidisciplinary and multi-physics, with multiple objectives involving coupled systems. Industrial products are complex and there are potentially hundreds of constraints. Treating the system as holistically as possible is of critical importance if invalid or poor designs are to be avoided.

As noted, system coupling can often be important. For example, as noted by Spalart and Bogue (2003) an ultimate aerospace vision would be to model the coupled airframe, engine and pilot interaction. The latter element also would need to include psychological response to events. The analysis might well encompass the need to account for aerodynamics, heat transfer and multi-phase flow. It could include the need to look at structural integrity in terms of peak stress, thermal or fatigue (both high and low cycle) failure and aeroelastic response. Product cost and weight are also key factors, the latter being highly critical for most aerospace applications.

The use of formal design optimization, involving numerous variations of design variables, has now become relatively standard industrial practice. Then, since coupled simulations are necessary low-order models become especially important. Also, there is the likelihood of geometric and boundary condition uncertainties and hence the need for a stochastic analysis level on top of potentially expensive deterministic simulation runs. Hence, this all furthers the need for lower order models. Therefore, with advanced simulations in mind, in this chapter, design optimization, coupled problems and low-order models are considered together. As part of low-order modelling it is necessary to consider the various truncated forms of the Navier-Stokes equations discussed in Chapter 2.

Notably, many industrial simulations involve a wide range of scales (i.e., they are multi-scale). They can also be multi-physics in nature. Hence, the modelling of multi-scale problems is also briefly considered along with more multi-physics aspects such as multi-phase flow, acoustics and fluid solid coupling. First design optimization is discussed. A critical aspect of this is producing low-order surrogate models. Hence, the design optimization discussion is followed by specifically considering low-order models. Then coupled calculations are considered, this again having the need for low-order models. Then, finally, more multi-physics and multi-scale modelling aspects are very briefly considered.

Design Optimization

Key Elements and General Process

Formal design optimization is important, giving an automatic process for verifiably seeking an improved design. The design optimization can be performed at various fidelities and stages of product design.