Abstract
We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.
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References
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, tenth printing, Dover, New York, 1972.
D.G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math. 17 (1969), 461–467.
F.J. Bureau, Differential equations with fixed critical points, Annali Mat. Pura Appl. 64 (1964), 229–364.
R. Conte, Invariant painlevé analysis of partial differential equations, Phys. Lett. A 140 (1989), 383–390.
R. Conte, Exact solutions of nonlinear partial differential equations by singularity analysis, in: A. Greco (ed.), Direct and inverse methods in nonlinear evolution equations, Lecture Notes in Physics, vol. 632, Springer Verlag, Berlin, 2003, pp. 1–83.
R. Conte, M. Musette, The Painlevé Handbook, second edition, Springer, Switzerland, 2020.
V.A. Galaktionov, S.A. Posashkov, Exact solutions and invariant spaces for nonlinear gradient diffusion equations, Comput. Math. Math. Phys. 34 (1994), 313–321.
B. Gambier, Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes, Acta Math. 33 (1910), 1–55.
R.L. Lemmer, P.G.L. Leac, The Painlevé test, hidden symmetries and the equation y″ + yy′ + ky 3 = 0, J. Phys. A 26 (1993), 5017–5024.
P.H. Maire, Étude d’une équation de diffusion non-linéaire. Application à la discrétisation de l’équation d’énergie cinétique turbulente pour un modèle de turbulence à une équation, 2001, p. 81, available from: https://hal-cea.archives-ouvertes.fr/cea-02931269/document Rapport CEA D01 03661.
P. Painlevé, Mémoire sur les équations différentielles dont l’intégrale générale est uniforme, Bull. Soc. Math. France 28 (1900), 201–261.
Y.B. Zel’dovich, Y. P. Raizer, Preface to the English edition, Physics of shock waves and high-temperature hydrodynamic phenomena, vol. 2, Academic Press, New York, 1967.
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Conte, R. Exact Solutions of a Nonlinear Diffusion Equation with Absorption and Production. J Nonlinear Math Phys 28, 171–181 (2021). https://doi.org/10.2991/jnmp.k.200922.008
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DOI: https://doi.org/10.2991/jnmp.k.200922.008