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

• URL: http://arxiv.org/abs/2109.10765v1
• Date: Wed, 22 Sep 2021 14:42:36 GMT
• Title: An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
• Authors: Federico Pichi and Francesco Ballarin and Gianluigi Rozza and Jan S. Hesthaven
• Abstract summary: We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. We propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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