Nonintrusive Reduced Order Modelling of Convective Boussinesq Flows

In this paper, we formulate three nonintrusive methods and systematically explore their performance in terms of the ability to reconstruct the quantities of interest and their predictive capabilities. The methods include deterministic dynamic mode decomposition, randomised dynamic mode decomposition and nonlinear proper orthogonal decomposition (NLPOD). We apply these methods to a convection dominated fluid flow problem governed by the Boussinesq equations. We analyse the reconstruction results primarily at two different times for considering different noise levels synthetically added into the data snapshots. Overall, our results indicate that, with a proper selection of the number of retained modes and neural network architectures, all three approaches make predictions that are in a good agreement with the full order model solution. However, we find that the NLPOD approach seems more robust for higher noise levels compared to both dynamic mode decomposition approaches.