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Group classification of one-dimensional nonisentropic equations of fluids with internal inertia

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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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Authors and Affiliations

  1. School of Science, Mae Fah Luang University, 57100, Chiangrai, Thailand

    P. Siriwat

  2. School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand

    S. V. Meleshko

Authors
  1. P. Siriwat
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  2. S. V. Meleshko
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Correspondence to S. V. Meleshko.

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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

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