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

TL;DR

This paper introduces a neural network-based reduced order modeling approach to analyze bifurcations in fluid dynamics, effectively capturing complex flow patterns and critical points in parametrized Navier-Stokes problems.

Contribution

It presents a novel POD-NN method for non-smooth solutions in nonlinear PDEs, enabling efficient bifurcation analysis in fluid flow problems with varying domain configurations.

Findings

Successfully identified bifurcation points in complex flow scenarios.

Accurately modeled flow pattern transitions at high Reynolds numbers.

Provided a non-intrusive tool for bifurcation diagram reconstruction.

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.