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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Nonlinear parametric models of viscoelastic fluid flows.

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This study introduces interpretable reduced-order models (ROMs) for complex viscoelastic fluid flows using the SINDy algorithm. The data-driven models accurately predict flow dynamics and extrapolate to unseen conditions, advancing non-Newtonian fluid mechanics.

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computational fluid dynamicsdata-driven modelsmachine learningreduced-order modelssparse identification of nonlinear dynamicsviscoelastic fluids

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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.