Agradecimentos: The authors of this work would like to acknowledge Fundação de Amparo à Pesquisa do Estado de São Paulo,FAPESP, for supporting the present work under research grants No. 2013/08293-7 and 2013/07375-0. The firstauthor is supported by FAPESP scholarships No. 2018/11410-9 and 2019/18809-7, and the second author is sup-ported by a scholarship from Conselho Nacional de Desenvolvimento Científico, CNPq Ver menos

An assessment of physics-based and data-driven reduced-order models (ROMs) is presented for the study of convective heat transfer in a rectangular cavity. Despite the simple geometrical configuration, the current setup offers increasingly rich dynamics as the thermal forcing is increased, thus making it a suitable candidate to evaluate the performance of ROMs. First, flow simulations are performed using a high-order spectral element method that will feed the ROMs with well-resolved temporal and spatial information. Proper orthogonal decomposition (POD) is applied to reduce the problem dimensionality for all models. The class of tested physics-based models include the Galerkin and least-squares Petrov–Galerkin (LSPG) methods that rely on projection of the Navier–Stokes and energy equations being solved. On the other hand, the data-driven methods applied in this work rely on regression of the governing equations, which are treated as a nonlinear dynamical system. The data-driven methods tested here include the sparse identification of nonlinear dynamics (SINDy) approach and a method recently proposed in literature based on deep neural networks (DNNs). All ROMs are able to represent the periodical temporal dynamics of a low Rayleigh number flow. However, the physics-based approaches demonstrate a better performance for a moderate Rayleigh number case with more complex flow dynamics, when several frequencies are excited in a non-periodical fashion Ver menos