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This article presents a general reduced order model (ROM) framework foraddressing fluid dynamics problems involving time-dependent geometricparametrisations. The framework integrates Proper Orthogonal Decomposition(POD) and Empirical Cubature Method (ECM) hyper-reduction techniques toeffectively approximate incompressible computational fluid dynamicssimulations. To demonstrate the applicability of this framework, we investigatethe behavior of a planar contraction-expansion channel geometry exhibitingbifurcating solutions known as the Coanda effect. By introducing time-dependentdeformations to the channel geometry, we observe hysteresis phenomena in thesolution.  The paper provides a detailed formulation of the framework, including thestabilised finite elements full order model (FOM) and ROM, with a particularfocus on the considerations related to geometric parametrisation. Subsequently,we present the results obtained from the simulations, analysing the solutionbehavior in a phase-space for the fluid velocity at a probe point, consideredas the Quantity of Interest (QoI). Through qualitative and quantitativeevaluations of the ROMs and hyper-reduced order models (HROMs), we demonstratetheir ability to accurately reproduce the complete solution field and the QoI.  While HROMs offer significant computational speedup, enabling efficientsimulations, they do exhibit some errors, particularly for testingtrajectories. However, their value lies in applications where the detection ofthe Coanda effect holds paramount importance, even if the selected bifurcationbranch is incorrect. Alternatively, for more precise results, HROMs with lowerspeedups can be employed.

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