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

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.

arXiv comment28 pages, 22 figures

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Cited by in corpus (5)

• Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
• Compatible finite element interpolated neural networks
• Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics
• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics
• Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs