POD-Galerkin modeling of a heated pool

Spent nuclear fuel elements contain a significant amount of fissile materials that gradually decompose generating heat and radiation. This decomposition occurs inside of deep water pools, where spent elements are cooled through natural convection. CFD calculation of all necessary cases is not feasible. Nevertheless, a light, fast and accurate model of this convection problem can be obtained utilizing Proper Orthogonal Decomposition (POD) and Galerkin Projection methods. Thus, we carry out our modeling as follows: i) Firstly, the high fidelity solver Star-CCM + is utilized to resolve the incompressible Boussinesq formulation of the pool. The results obtained constitute a set of solutions available at discrete times for each variable. ii) Subsequently, these solutions are utilized to build a special basis, which constitutes the POD. This is built considering an optimal linear combination of the solutions at different times. Notably, each reduced set of components of the basis allows for the reproduction of a maximum of the dynamics of the variables. iii) Thirdly, the system of equations is projected in this basis, Galerkin Projection. A Reduced Order Model (ROM) can be created using a small amount of the components, sufficient for the required accuracy. This simplified model is thus mathematically sound, and derived from first principles. Finally, the results of the model are compared with high fidelity solutions. The assessment includes the capabilities of the model to reproduce transients and to approach the final steady state. Additionally, we evaluate the performance of the MPI-parallelized software generated.