Data-Driven Discovery of Normal Forms in Viscoelastic Flows in Cross-Slot Configurations

Abstract

Viscoelastic flows arising in industrial processing and lab-on-a-chip applications often exhibit elastic symmetry-breaking instabilities that generate complex nonlinear dynamics. In cross-slot geometries, this behavior provides a canonical setting for pitchfork bifurcations, in which the flow asymmetry parameter q(t) transitions from a symmetric to an asymmetric state as elastic stresses overcome viscous damping. The governing dimensionless parameters, the Weissenberg number (Wi) and the viscosity ratio (beta) , quantify the relative contributions of elastic and viscous effects. While such instabilities are well documented in experiments and simulations, constructing reduced-order dynamical models that consistently organize the bifurcation dynamics across material conditions remains an open challenge. In this thesis, a data-driven framework is developed to identify low-dimensional normal-form evolution equations governing the dynamics of q(t) from computational fluid dynamics time-series data spanning multiple (Wi, beta) conditions. Three complementary model discovery approaches are investigated: Dimensionless Sparse Identification of Nonlinear Dynamics (SINDy), Symbolic Regression, and a nonlinear optimization-based integrator. These methods are used to recover reduced dynamical models directly from data while preserving the underlying symmetry-breaking structure. Model performance is assessed through time-series and bifurcation diagram reconstruction along with steady-state bifurcation metrics. The results demonstrate method-dependent accuracy and show that shifted formulations improve alignment of bifurcation onset across material conditions. Overall, this work illustrates how data-driven model discovery applied to CFD data can yield interpretable reduced-order descriptions of viscoelastic instabilities relevant to microscale flow control and industrial processing.