Verification/validation and quantification of uncertainties in numerical simulations

The aim of this course is to introduce engineering students to verification/validation and uncertainty quantification approaches (VetV-UQ). The concept of verification/validation is important for any industrial company wishing to make efficient use of simulation resources, in order to avoid the multiplication of potentially dangerous, polluting or simply costly experiments. Verification is the process of determining whether the numerical model, obtained by discretizing the continuous mathematical model of the physical phenomenon, and the calculation code under consideration can be used to represent the mathematical model with sufficient accuracy. Validation is the process of determining whether a model of a physical phenomenon represents the actual physical phenomenon with sufficient accuracy for the model's intended use. More concisely, verification deals with mathematics, while validation deals with physics. Thus, the first stage of verification is numerical analysis, and consists in showing that the code converges towards a model that is representative of the physics we are trying to solve. Uncertainty analysis is the main tool that will enable us to carry out the validation step.
In the context of uncertainty quantification, we will present the classical approach based on the "ABCD" approach. Step A consists in defining the physical phenomenon to be simulated. In step B, we quantify our sources of uncertainty, which we propagate in step C. Step D will be dedicated to a sensitivity analysis of the parameters.
The tools to be presented in this session will concern the planning of experiments for the creation of metamodels, the construction of metamodels (or response surfaces), Monte Carlo methods applied to the propagation of uncertainties, and tools for qualitative and quantitative sensitivity analysis.

Numerical simulation using NS code (Fluent, OpenFoam).
Classical statistical and probabilistic tools.