Uncertainty Quantification in CFD: The Matrix of Knowledge

The main difference between an experimental study and the corresponding numerical simulation is that the latter is usually considered a deterministic exercise, while the experiments are inherently affected by uncertainty. Despite this, the usage of numerical simulations is gaining more and more importance in aero-engine research thanks to their growing accuracy and accessibility. It must be underlined that even the most sophisticated numerical simulation cannot consider by default the impact of the uncertainties. Therefore, uncertainty quantification (UQ) techniques are increasingly coupled with deterministic calculations to include the most relevant variabilities. The overall goal of UQ is to investigate the impact of aleatory and epistemic uncertainties on a system response quantity of interest. The lesson learnt after applying UQ techniques to the numerical study of several aero-engine components is that to fully understand simulation results, it is imperative to incorporate uncertainty from the very beginning of the numerical procedure. To demonstrate that outcome, this chapter presents a discussion about the concepts of code verification and calculation validation, with a special interest in the analysis of the observed order of accuracy. A discussion about the definitions of aleatory and epistemic uncertainty follows, aiming at defining a common ground to start with the definition of what is called “uncertainty quantification” in engineering problems. A detailed list of limitations in deterministic computational fluid dynamics is also included in the chapter.