Shallow‐water equations with complete Coriolis force: Group properties and similarity solutions

Paliathanasis, Andronikos

doi:10.1002/mma.7168

Cited by 8 publications

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References 50 publications

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“…The Lie symmetries for the one-dimensional shallow-water system were determined in [23]. The complete symmetry classification of shallow-water equations for a twodimensional flow was performed in [24], while the same problem in a rotating frame with non-zero Coriolis component was investigated in [25], while a varying bottom topography was considered in [26]; see also [27][28][29]. The group properties for the hyperbolic equations of two-phase flow models of fluid dynamics were investigated in [30][31][32].…”

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confidence: 99%

Symmetry Analysis for the 2D Aw-Rascle Traffic-Flow Model of Multi-Lane Motorways in the Euler and Lagrange Variables

Paliathanasis

2023

Symmetry

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A detailed symmetry analysis is performed for a microscopic model used to describe traffic flow in two-lane motorways. The traffic flow theory employed in this model is a two-dimensional extension of the Aw-Rascle theory. The flow parameters, including vehicle density, and vertical and horizontal velocities, are described by a system of first-order partial differential equations belonging to the family of hydrodynamic systems. This fluid-dynamics model is expressed in terms of the Euler and Lagrange variables. The admitted Lie point symmetries and the one-dimensional optimal system are determined for both sets of variables. It is found that the admitted symmetries for the two sets of variables form different Lie algebras, leading to distinct one-dimensional optimal systems. Finally, the Lie symmetries are utilized to derive new similarity closed-form solutions.

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