Non-intrusive reduced order models for the accurate prediction of bifurcating phenomena in compressible fluid dynamics

TL;DR

This paper develops non-intrusive reduced order models to accurately predict bifurcations in compressible fluid dynamics, validated against high-fidelity simulations using the Discontinuous Galerkin method.

Contribution

It introduces and compares two non-intrusive reduced order modeling techniques for bifurcation prediction in compressible flows, demonstrating their effectiveness near non-smooth bifurcation points.

Findings

Both models agree well with full-order simulations near bifurcation points.

The models effectively capture non-smooth bifurcating solutions.

High-fidelity simulations validate the reduced order models' accuracy.

Abstract

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations discretised with the Discontinuous Galerkin method. On the other side, from a numerical modelling point of view, two different non-intrusive reduced order modelling techniques are employed to predict the overall behaviour of the bifurcation. Both approaches showed good agreement with full-order simulations even in proximity of the bifurcating points where the solution is particularly non-smooth.