On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics

TL;DR

This paper introduces a reduced basis approach to efficiently compute bifurcation and stability diagrams in incompressible fluid dynamics, significantly reducing computational complexity for low Reynolds number flows.

Contribution

It presents a general reduced basis framework tailored for bifurcation problems in fluid dynamics, with specific application and validation on cavity flow at low Reynolds numbers.

Findings

Reduced basis method accurately predicts bifurcation points.

Significant reduction in computational time compared to full models.

Successful validation on benchmark cavity flow problem.

Abstract

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.