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Volume 37, Issue 3
Three Dimensional Dynamics of Polar Fluids: A Lattice Boltzmann Approach

Michele La Rocca, Andrea Montessori & Pietro Prestininzi

DOI: 10.4208/cicp.OA-2024-0216

Commun. Comput. Phys., 37 (2025), pp. 623-642.

Published online: 2025-03

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  • Abstract

In this paper we propose a Lattice-Boltzmann-based mesoscopic model for the three-dimensional flow of an incompressible polar fluid.
The mesoscopic model is equivalent to the usual incompressible three-dimensional Navier-Stokes equation coupled with the angular momentum equation, which describes the evolution of the angular velocity vector of the fluid particles.
The proposed model is applied to investigate the effects of the fluid polar structure on three steady flows: the steady Couette and Poiseuille flows in a square channel and the three-dimensional lid-driven cavity flow at $Re=100,$ $Re=400.$
The effects of the fluid polar structure on the above mentioned flows are investigated by varying the relevant dimensionless parameters: the coupling parameter $N$ and the geometric parameter $L.$
Results are consistent with the predictions of the theory of polar fluids. In particular, it is shown for the three-dimensional lid-driven cavity flow that the effect of the coupling parameter $N$ is to lower the effective Reynolds number and thus to increase the viscosity.

  • Keywords

Computational fluid dynamics, lattice Boltzmann method, polar fluids.

  • AMS Subject Headings

76D05, 76M25, 76R05, 76D99

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-37-623, author = {Rocca , Michele LaMontessori , Andrea and Prestininzi , Pietro}, title = {Three Dimensional Dynamics of Polar Fluids: A Lattice Boltzmann Approach}, journal = {Communications in Computational Physics}, year = {2025}, volume = {37}, number = {3}, pages = {623--642}, abstract = {

In this paper we propose a Lattice-Boltzmann-based mesoscopic model for the three-dimensional flow of an incompressible polar fluid.
The mesoscopic model is equivalent to the usual incompressible three-dimensional Navier-Stokes equation coupled with the angular momentum equation, which describes the evolution of the angular velocity vector of the fluid particles.
The proposed model is applied to investigate the effects of the fluid polar structure on three steady flows: the steady Couette and Poiseuille flows in a square channel and the three-dimensional lid-driven cavity flow at $Re=100,$ $Re=400.$
The effects of the fluid polar structure on the above mentioned flows are investigated by varying the relevant dimensionless parameters: the coupling parameter $N$ and the geometric parameter $L.$
Results are consistent with the predictions of the theory of polar fluids. In particular, it is shown for the three-dimensional lid-driven cavity flow that the effect of the coupling parameter $N$ is to lower the effective Reynolds number and thus to increase the viscosity.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0216}, url = {http://global-sci.org/intro/article_detail/cicp/23916.html} }
TY - JOUR T1 - Three Dimensional Dynamics of Polar Fluids: A Lattice Boltzmann Approach AU - Rocca , Michele La AU - Montessori , Andrea AU - Prestininzi , Pietro JO - Communications in Computational Physics VL - 3 SP - 623 EP - 642 PY - 2025 DA - 2025/03 SN - 37 DO - http://doi.org/10.4208/cicp.OA-2024-0216 UR - https://global-sci.org/intro/article_detail/cicp/23916.html KW - Computational fluid dynamics, lattice Boltzmann method, polar fluids. AB -

In this paper we propose a Lattice-Boltzmann-based mesoscopic model for the three-dimensional flow of an incompressible polar fluid.
The mesoscopic model is equivalent to the usual incompressible three-dimensional Navier-Stokes equation coupled with the angular momentum equation, which describes the evolution of the angular velocity vector of the fluid particles.
The proposed model is applied to investigate the effects of the fluid polar structure on three steady flows: the steady Couette and Poiseuille flows in a square channel and the three-dimensional lid-driven cavity flow at $Re=100,$ $Re=400.$
The effects of the fluid polar structure on the above mentioned flows are investigated by varying the relevant dimensionless parameters: the coupling parameter $N$ and the geometric parameter $L.$
Results are consistent with the predictions of the theory of polar fluids. In particular, it is shown for the three-dimensional lid-driven cavity flow that the effect of the coupling parameter $N$ is to lower the effective Reynolds number and thus to increase the viscosity.

Rocca , Michele LaMontessori , Andrea and Prestininzi , Pietro. (2025). Three Dimensional Dynamics of Polar Fluids: A Lattice Boltzmann Approach. Communications in Computational Physics. 37 (3). 623-642. doi:10.4208/cicp.OA-2024-0216
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