Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics

Abstract

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behavior of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution. The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behavior in a phase-space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI. While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

References in corpus (12)

• A New Selection Operator for the Discrete Empirical Interpolation Method -- improved a priori error bound and extensions
• A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics
• An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
• A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions
• Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology
• On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics
• A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations
• Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems
• CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models
• Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
• Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature
• A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady Navier-Stokes problems

Cited by in corpus (2)

• Parallel Reduced Order Modeling for Digital Twins using High-Performance Computing Workflows
• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics