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<p>Accurately resolving spatially inhomogeneous flows is one of the essential roles of computational rheology. Compared to conventional flow predictions using constitutive models (CMs), multiscale simulations (MSSs), where mesoscopic models are embedded in macroscopic computational domains, offer accurate predictions but are accompanied by high computational costs. To avoid the computational issue in these MSSs (which we refer to as “full”-MSSs), we employed machine learning (ML) techniques, which we denote as “ML”-MSS, to predict spatially inhomogeneous flows. We obtained approximate CMs using a sparse identification algorithm for training data numerically generated by the dumbbell-based mesoscopic model with the Hookean or finite extensible nonlinear elastic (FENE) spring. Our sparse identification algorithm accurately identifies the CM for the dumbbell model with the Hookean spring and provides an approximate CM that reproduces the shear rheology of the dumbbell model with the FENE spring. The ML-MSSs with these CMs were compared to the full-MSSs for a flow between parallel plates driven by an external force. We confirmed that the relative error in the primary velocity along the centerline between ML-MSS and full-MSS is within approximately 20%, indicating the fundamental validity of our data-driven approach, with a computational time equivalent to that of a conventional approach employing CMs.</p>

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Multiscale simulations for viscoelastic fluids with approximate constitutive models derived by a sparse identification method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月30日

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  • Takeshi Sato,
  • Souta Miyamoto

摘要

Accurately resolving spatially inhomogeneous flows is one of the essential roles of computational rheology. Compared to conventional flow predictions using constitutive models (CMs), multiscale simulations (MSSs), where mesoscopic models are embedded in macroscopic computational domains, offer accurate predictions but are accompanied by high computational costs. To avoid the computational issue in these MSSs (which we refer to as “full”-MSSs), we employed machine learning (ML) techniques, which we denote as “ML”-MSS, to predict spatially inhomogeneous flows. We obtained approximate CMs using a sparse identification algorithm for training data numerically generated by the dumbbell-based mesoscopic model with the Hookean or finite extensible nonlinear elastic (FENE) spring. Our sparse identification algorithm accurately identifies the CM for the dumbbell model with the Hookean spring and provides an approximate CM that reproduces the shear rheology of the dumbbell model with the FENE spring. The ML-MSSs with these CMs were compared to the full-MSSs for a flow between parallel plates driven by an external force. We confirmed that the relative error in the primary velocity along the centerline between ML-MSS and full-MSS is within approximately 20%, indicating the fundamental validity of our data-driven approach, with a computational time equivalent to that of a conventional approach employing CMs.