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Generalized Lagrangian heterogeneous multiscale modelling of complex fluids

Published online by Cambridge University Press:  10 August 2023

Nicolas Moreno Open the ORCID record for Nicolas Moreno [Opens in a new window]  and
Marco Ellero Open the ORCID record for Marco Ellero [Opens in a new window]
Nicolas Moreno*
Affiliation:
Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo, 14, 48400 Bilbao, Spain
Marco Ellero*
Affiliation:
Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo, 14, 48400 Bilbao, Spain IKERBASQUE, Basque Foundation for Science, Calle de Maria Dias de Haro 3, 48013 Bilbao, Spain Zienkiewicz Center for Computational Engineering (ZCCE), Swansea University, Bay Campus, Swansea SA1 8EN, UK
*
†Email addresses for correspondence: nmoreno@bcamath.org, mellero@bcamath.org
†Email addresses for correspondence: nmoreno@bcamath.org, mellero@bcamath.org
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Abstract

We introduce a fully Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio/temporal scales, such as polymeric solutions and multiphasic systems. The proposed approach discretizes the fluctuating Navier–Stokes equations in a particle-based setting using smoothed dissipative particle dynamics (SDPD). This multiscale method uses microscopic information derived on-the-fly to provide the stress tensor of the momentum balance in a macroscale problem, therefore bypassing the need for approximate constitutive relations for the stress. We exploit the intrinsic multiscale features of SDPD to account for thermal fluctuations as the characteristic size of the discretizing particles decreases. We validate the LHMM using different flow configurations (reverse Poiseuille flow, flow passing a cylinder array and flow around a square cavity) and fluid (Newtonian and non-Newtonian). We show the framework's flexibility to model complex fluids at the microscale using multiphase and polymeric systems. We also show that stresses are adequately captured and passed from micro to macro scales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales.

JFM classification

Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 969 , 25 August 2023 , A2
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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