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arXiv · 2109.10765

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

Federico Pichi·Francesco Ballarin·Gianluigi Rozza·Jan S. Hesthaven
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Abstract

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we study the Navier-Stokes equations describing: (i) the Coanda effect in a channel, and (ii) the lid driven triangular cavity flow, in a physical/geometrical multi-parametrized setting, considering the effects of the domain's configuration on the position of the bifurcation points. Finally, we propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution. Exploiting such detection tool, we are able to efficiently obtain information about the pattern flow behaviour, from symmetry breaking profiles to attaching/spreading vortices, even at high Reynolds numbers.

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Federico Pichi, Francesco Ballarin, Gianluigi Rozza, Jan S. Hesthaven. 2021-09-22. An artificial neural network approach to bifurcating phenomena in computational fluid dynamics. https://doi.org/10.1016/j.compfluid.2023.105813

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