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

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced basis. In the few existing works dealing with model reduction t...

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Bibliographic Details
Published inarXiv.org
Main Authors Allery, Cyrille, Beghein, Claudine, Dubot, Claire, Dubot, Fabien
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.07.2023
Subjects
Artificial neural networks
Barriers
Darcys law
Galerkin method
Laminar flow
Model reduction
Multilayer perceptrons
Neural networks
Numerical models
Porous media
Proper Orthogonal Decomposition
Reduced order models
Sampling
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Summary:This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced basis. In the few existing works dealing with model reduction techniques applied to flows in porous media, flows were described by Darcy's law and the non linear Forchheimer term was neglected. This last term cannot be expressed in reduced form during the Galerkin projection phase. Indeeed, at each new time step, the norm of the velocity needs to be recalculated and projected, which significantly increases the computational cost, rendering the reduced model inefficient. To overcome this difficulty, we propose to model the projected Forchheimer term with artificial neural networks. Moreover in order to build a stable ROM, the influence of unresolved modes and pressure variations are also modeled using a neural network. Instead of separately modeling each term, these terms were combined into a single residual, which was modeled using the multilayer perceptron method (MLP). The validation of this approach was carried out for laminar flow past a porous obstacle in an unconfined channel. The proposed ROM coupled with MLP approach is able to accurately predict the dynamics of the flow while the standard ROM yields wrong results. Moreover, the ROM MLP method improves the prediction of flow for Reynols number that are not included in the sampling and for times longer than sampling times.
ISSN:2331-8422