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This paper deals with the numerical modeling of flow around and through aporous obstacle by a reduced order model (ROM) obtained by Galerkin projectionof the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD)reduced basis. In the few existing works dealing with model reductiontechniques applied to flows in porous media, flows were described by Darcy'slaw and the non linear Forchheimer term was neglected. This last term cannot beexpressed in reduced form during the Galerkin projection phase. Indeeed, ateach new time step, the norm of the velocity needs to be recalculated andprojected, which significantly increases the computational cost, rendering thereduced model inefficient. To overcome this difficulty, we propose to model theprojected Forchheimer term with artificial neural networks. Moreover in orderto build a stable ROM, the influence of unresolved modes and pressurevariations are also modeled using a neural network. Instead of separatelymodeling each term, these terms were combined into a single residual, which wasmodeled using the multilayer perceptron method (MLP). The validation of thisapproach was carried out for laminar flow past a porous obstacle in anunconfined channel. The proposed ROM coupled with MLP approach is able toaccurately predict the dynamics of the flow while the standard ROM yields wrongresults. Moreover, the ROM MLP method improves the prediction of flow forReynols number that are not included in the sampling and for times longer thansampling times.

Solving flows in porous media with a POD-Galerkin reduced order model coupled with multilayer perceptron