Sensitivity analysis for a thermohydrodynamic model: uncertainty analysis and parameter estimation

Abstract

This paper proposes an efficient computational strategy to deal with uncertainty propagation problems for the Navier–Stokes equations coupled with a temperature equation based on a sensitivity analysis technique model. Sensitivity analysis allows one to investigate how the model response in a point is affected by a change in the boundary conditions on the temperature, the heat capacity, the thermal conductivity, and the thermal diffusivity under the hypothesis of a small variance of the input parameters. The variance can be estimated with just one simulation of the state and as many simulations of the sensitivity as there are uncertain parameters. We focused on the benchmark problem of natural convection in a square cavity, also known as the de Vahl Davis problem. Various areas of the domain were analysed to determine the relative influence of each parameter on temperature and velocity. We use the open-source code TrioCFD to simulate the state equations and a specific module is developed for the sensitivity equations.