Abstract:
Using an example of a model of shallow water theory, we show that the compatibility analysis of Hugoniot conditions for various basic systems of conservation laws in a coordinate system moving together with a strong discontinuity can lead to erroneous results. This is connected with the hierarchy of conservation laws of shallow water theory under a Galilean transformation, by which the law of conservation of the total energy is unconditionally noninvariant under this transformation. As a result, the Hugoniot condition corresponding to this conservation law depends on movement speed of the inertial coordinate system. It is shown that the specified defect of the classical model of shallow water theory is absent in the vortex shallow water model suggested by V. M. Teshukov.
Keywords:
conservation laws of shallow water theory, Galilean relativity principle, classical and weak solutions.
Citation:
V. V. Ostapenko, “Conservation laws of shallow water theory and the Galilean relativity principle”, Sib. Zh. Ind. Mat., 17:1 (2014), 99–113; J. Appl. Industr. Math., 8:2 (2014), 274–286
\Bibitem{Ost14}
\by V.~V.~Ostapenko
\paper Conservation laws of shallow water theory and the Galilean relativity principle
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 1
\pages 99--113
\mathnet{http://mi.mathnet.ru/sjim823}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379258}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 2
\pages 274--286
\crossref{https://doi.org/10.1134/S1990478914020148}
Linking options:
https://www.mathnet.ru/eng/sjim823
https://www.mathnet.ru/eng/sjim/v17/i1/p99
This publication is cited in the following 4 articles:
Vladimir V. Ostapenko, “Asymptotics of solutions to the problem of fluid outflow from a rectangular duct”, Physics of Fluids, 33:4 (2021)
N. H. Sweilam, D. M. ElSakout, M. M. Muttardi, “High-Resolution Schemes for Stochastic Nonlinear Conservation Laws”, Int. J. Appl. Comput. Math, 6:1 (2020)
G. L. Richard, M. Gisclon, C. Ruyer-Quil, J. P. Vila, “Optimization of consistent two-equation models for thin film flows”, Eur. J. Mech. B-Fluids, 76 (2019), 7–25
G. L. Richard, C. Ruyer-Quil, J. P. Vila, “A three-equation model for thin films down an inclined plane”, J. Fluid Mech., 804 (2016), 162–200
Citation in format AMSBIB
Contact us: