Abstract
A systematic application of the group analysis method for modeling fluids with internal inertia is presented. The equations studied include models such as the nonlinear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small volume concentration of gas bubbles (Iordanski Zhurnal Prikladnoj Mekhaniki i Tekhnitheskoj Fiziki 3, 102–111, 1960; Kogarko Dokl. AS USSR 137, 1331–1333, 1961; Wijngaarden J. Fluid Mech. 33, 465–474, 1968), and the dispersive shallow water model (Green and Naghdi J. Fluid Mech. 78, 237–246, 1976; Salmon 1988). These models are obtained for special types of the potential function \({W(\rho,\dot \rho,S)}\) (Gavrilyuk and Teshukov Continuum Mech. Thermodyn. 13, 365–382, 2001). The main feature of the present paper is the study of the potential functions with W S ≠ 0. The group classification separates these models into 73 different classes.
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Communicated by Andreas Öchsner.
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Siriwat, P., Meleshko, S.V. Group classification of one-dimensional nonisentropic equations of fluids with internal inertia. Continuum Mech. Thermodyn. 24, 115–148 (2012). https://doi.org/10.1007/s00161-011-0209-6
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DOI: https://doi.org/10.1007/s00161-011-0209-6