Reduced order modeling approach for parametrized thermal-hydraulics problems: inclusion of the energy equation in the POD-FV-ROM method

The trade-off between solution accuracy and computational burden is fundamental in numerical simulations, in particular for the fluid dynamics field. The aim of this work is to develop a Reduced Order Model (ROM) for heat transfer problems in Computational Fluid Dynamics (CFD). Such objective is achieved by including the energy equation in the POD-FV-ROM, a reduced order technique for Navier-Stokes equations described in Lorenzi et al. (2016). The technique, ad-hoc developed for the Finite Volume (FV) framework, relies on the Proper Orthogonal Decomposition (POD) and the projection of the physical fields onto subspaces of finite dimensions. Besides the extension to thermal-hydraulics, the work focuses on the capability to handle parametrized boundary conditions, especially the Neumann ones. To this aim a new approach is proposed and tested in two cases. In each case studied, the relative L² norms of the differences for p, T, U resulted to be below 1% in steady state conditions.