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Poisson and Symplectic Structures, Hamiltonian Action, Momentum and Reduction Read chapter Read first chapter

2021 | OriginalPaper | Chapter

5. Critical Phenomena in Darcy and Euler Flows of Real Gases

Authors : Valentin V. Lychagin, Mikhail D. Roop

Published in: Differential Geometry, Differential Equations, and Mathematical Physics

Publisher: Springer International Publishing

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Abstract

This paper is a survey article on some recent results obtained by the authors in the field of gas flows through porous media described by the Darcy law and flows of inviscid gases described by Euler equations. We explicitly formulate thermodynamics in terms of contact and symplectic geometry and show the link between thermodynamics and measurement theory. The methods provided by the geometrical reformulation of thermodynamics are applied to the analysis of various models of real gases, and special attention is paid to phase transitions. We provide explicit methods of finding solutions for the Dirichlet filtration problem and Euler flows and show how thermodynamics of gases under consideration emerges along the gas flow. In particular, we find the locations for different phases of the medium.

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previous chapter Finite Dimensional Dynamics of Evolutionary Equations with Maple
next chapter Differential Invariants for Flows of Fluids and Gases
Literature
1.
Lychagin, V.: Adiabatic filtration of an ideal gas in a homogeneous and isotropic porous medium. Glob. Stoch. Anal. 6(1), 23–31 (2019)
2.
3.
Lychagin, V., Roop, M.: Steady filtration of Peng-Robinson gases in a porous medium. Glob. Stoch. Anal. 6(2), 59–68 (2019)
4.
Lychagin, V., Roop, M.: Phase transitions in filtration of real gases. arXiv:1903.00276
5.
6.
Scheidegger, A.E.: The physics of flow through porous media. Revised edition. The Macmillan Co., New-York (1960)
7.
Leibenson, L.S.: Motion of natural liquids and gases in a porous medium. Gostekhizdat, Moscow (1947)
8.
Muskat, M.: The Flow of Homogeneous Fluids Through Porous Media. McGraw-Hill, New-York (1937)MATH
9.
Maikov, I.L., Zaichenko, V.M., Torchinsky, V.M.: Theoretical Investigations of Filtration Process of Hydrocarbon Mixtures in Porous Media. 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, 1266–1269 (2012)
10.
Kachalov, V.V, Molchanov, D.A., Sokotushchenko, V.N., Zaichenko, V.M.: Mathematical modeling of gas-condensate mixture filtration in porous media taking into account non-equilibrium of phase transitions. Journal of Physics: Conference Series. 774(1) (2016)
11.
Duyunova, A., Lychagin, V.,Tychkov, S.: Non-stationary adiabatic filtration of gases in porous media. arXiv:1908.09316
12.
Landau, L.: New Exact Solution of the Navier-Stokes Equations. Doklady Akademii Nauk SSSR. 43 311–314 (1944) (in Russian)MathSciNet
13.
Broman, G.I., Rudenko, O.: Submerged Landau jet: exact solutions, their meaning and application. Uspekhi Fizicheskikh Nauk. 80(1), 97–104 (2010) (in Russian)CrossRef
14.
Vinogradov, A.M., Krasilshchik, I.S.: Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. Factorial, Moscow (1997)
15.
Krasilshchik, I.S., Lychagin, V.V., Vinogradov, A.M.: Geometry of Jet Spaces and Nonlinear Partial Differential Equations. Gordon and Breach Science Publishers (1986)
16.
Squire, H.B.: The round laminar jet. Quarterly Journal of Mechanics and Applied Mathematics. 4(3), 321–329 (1951)MathSciNetCrossRef
17.
18.
Gorinov, A., Lychagin, V., Roop, M., Tychkov, S.: Gas Flow with Phase Transitions: Thermodynamics and the Navier-Stokes Equations. In: Kycia, R., Ulan, M., Schneider, E. (eds.) Nonlinear PDEs, Their Geometry, and Applications., pp. 229–241. Birkhauser, Cham (2019)
19.
Lychagin, V.: Contact Geometry, Measurement and Thermodynamics. In: Kycia, R., Ulan, M., Schneider, E. (eds.) Nonlinear PDEs, Their Geometry, and Applications., pp. 3–52. Birkhauser, Cham (2019)CrossRef
20.
Mrugala, R.: Geometrical formulation of equilibrium phenomenological thermodynamics. Reports on Mathematical Physics. 14(3), 419–427 (1978)MathSciNetCrossRef
21.
Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Reviews of Modern Physics. 67(3), 605–659 (1978)MathSciNetCrossRef
22.
Peng, B.Y., Robinson, D.B.: A New Two-Constant Equation of State. Industrial and Engineering Chemistry: Fundamentals. 15 59–64 (1976)CrossRef
23.
Redlich, O., Kwong, J.N.S.: On the Thermodynamics of Solutions. Chem. Rev. 44(1), 233–244 (1949).CrossRef
Metadata
Title
Critical Phenomena in Darcy and Euler Flows of Real Gases
Authors
Valentin V. Lychagin
Mikhail D. Roop
Copyright Year
2021
Book
Differential Geometry, Differential Equations, and Mathematical Physics

Print ISBN: 978-3-030-63252-6

Electronic ISBN: 978-3-030-63253-3

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-63253-3_5

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