Nonlinear parametric models of viscoelastic fluid flows.

Area of Science:

• Fluid Mechanics
• Non-Newtonian Fluid Dynamics
• Computational Science

Background:

• Reduced-order models (ROMs) are computationally efficient for Newtonian fluids but underutilized for complex non-Newtonian viscoelastic flows.
• Viscoelastic flows present challenges like instabilities and bifurcations due to coupled viscous and elastic forces, requiring significant computational resources.
• Existing methods struggle to capture the intricate dynamics of viscoelastic fluids across various flow parameters.

Purpose of the Study:

• To develop interpretable reduced-order models (ROMs) for viscoelastic fluid flows using the sparse identification of nonlinear dynamics (SINDy) algorithm.
• To demonstrate the capability of data-driven surrogate models in predicting transient evolution and reconstructing spatial flow fields.
• To create a parametric model that captures dynamic variations with the Weissenberg number and extrapolates to high Weissenberg numbers.

Main Methods:

• Application of the sparse identification of nonlinear dynamics (SINDy) algorithm to identify governing equations from data.
• Development of data-driven surrogate models for a benchmark oscillatory viscoelastic flow in a four-roll mill using the Oldroyd-B fluid model.
• Parametrization of the nonlinear model to capture dynamics as a function of the Weissenberg number.

Main Results:

• Successfully demonstrated the effectiveness of SINDy-based ROMs in predicting transient flow evolution and reconstructing spatial flow fields.
• Developed a fully parametric nonlinear model capable of capturing dynamic variations with the Weissenberg number.
• Showcased the model's ability to extrapolate and accurately predict dominant dynamics even for high Weissenberg numbers, beyond the training data regime.

Conclusions:

• The SINDy algorithm provides a powerful tool for creating interpretable ROMs for complex viscoelastic flows.
• Data-driven surrogate models offer a computationally efficient alternative for analyzing non-Newtonian fluid dynamics.
• This methodology represents a significant advancement in applying machine learning to viscoelastic flow modeling and analysis.