Analysis of uncertainty of a heated pool via reduced order modelling*

In this article the uncertainty on the calculation of three dimensional spatio-temporal evolution of Raileigh-Bènard convection is analyzed. This assessment is carried out through the creation of a surrogate --fast-- model for the thermal natural convection of pools.                        

The assessment of the inaccuracy and sensitivity of simulations of natural convection in pools is of the highest importance for the nuclear industry and concretely for the design of the  reactors of the IV generation. 

The model is build utilizing the Proper Orthogonal Decomposition coupled with the Galerkin projection. The most energetic modes are derived from a high fidelity CFD calculation. The governing equations are henceforth projected into the manifold generated.

Once the model is available, we consider uncertainties on the dimensionless numbers, Re, Pr, Ra, and on the initial conditions. The expected result and its uncertainty is computed by Monte-Carlo method, calculating hundreds of solutions of the initial value problem with the surrogate model.