Recent Results on Wave Propagation in Continuum Models

Ruggeri, Tommaso

doi:10.1007/978-3-7091-3004-9_4

Cited by 4 publications

(8 citation statements)

References 27 publications

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“…The Rankine Hugoniot conditions for a monatomic gas in the framework of the extended thermodynamic have been obtained in [2] where it is shown that, by considering the propagation into an equilibrium state characterized by ρ • p • v • = q • = σ • = 0 and introducing the adimensional variables…”

Section: The Point Explosion Problemmentioning

confidence: 99%

“…Also, because of the difficulty to manage the whole system, the study of non-linear effects on wave propagation, very often, is carried on by considering the one dimensional case and assuming the state where the perturbation propagate is constant and characterizing an equilibrium state [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…We remark that the greater value of w represents a lower bound for the volume ratio and it is the only one satisfying the admissibility criterion of Lax for the shock [1,2].…”

mentioning

confidence: 97%

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Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas

Donato

Ruggeri

2000

Journal of Mathematical Analysis and Applications

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We consider the equations of a monoatomic gas, in the context of the extended thermodynamic theory, with spherical symmetry and we look for similarity solutions. The classical problem of the point explosion is considered in order to get some qualitative information due to the presence of the heat flux and the dissipation. It seems that, despite to the classical case, a sub-shock formation cannot be avoided.

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Section: The Point Explosion Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas

Donato

Ruggeri

2000

Journal of Mathematical Analysis and Applications

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“…Moreover, it was shown that for shock waves with a Mach number beyond some critical value, the shock structure is lost in contradiction to the Navier-Fourier-Stokes equations where the shock is preserved whatever the value of the Mach number. In the 13-moment approximation, which is equivalent to taking q and the traceless 0 P v as variables, the critical Mach number [Ruggeri 1993;Müller 1998] is Ma = 1.65 and this value increases only slowly when the number of moments is increased [Weiss 1990]. Another criticism concerns expression (4.18) of the entropy flux.…”

mentioning

confidence: 99%

Early history of extended irreversible thermodynamics (1953–1983): An exploration beyond local equilibrium and classical transport theory

Lebon

Jou

2014

EPJ H

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Abstract. This paper gives a historical account of the early years of extended irreversible thermodynamics (EIT). The salient features of this formalism are to upgrade the thermodynamic fluxes of mass, momentum, energy, and others, to the status of independent variables, and to explore the consistency between generalized transport equations and a generalized version of the second law of thermodynamics. This requires going beyond classical irreversible thermodynamics by redefining entropy and entropy flux. EIT provides deeper foundations, closer relations with microscopic formalisms, a wider spectrum of applications, and a more exciting conceptual appeal to non-equilibrium thermodynamics. We first recall the historical contributions by Maxwell, Cattaneo, and Grad on generalized transport equations. A thermodynamic theory wide enough to cope with such transport equations was independently proposed between 1953 and 1983 by several authors, each emphasizing different kinds of problems. In 1983, the first international meeting on this theory took place in Bellaterra (Barcelona). It provided the opportunity for the various authors to meet together for the first time and to discuss the common points and the specific differences of their previous formulations. From then on, a large amount of applications and theoretical confirmations have emerged. From the historical point of view, the emergence of EIT has been an opportunity to revisit the foundations and to open new avenues in thermodynamics, one of the most classical and well consolidated physical theories.a

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“…According to P. Lax (see [6,5,13,19]), completely exceptionality is what marks the line between "genuinely nonlinear" systems and nonlinear systems "displaying a linear behavior".…”

Section: Introductionmentioning

confidence: 99%

Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution

Gutt

Manno

Moreno

2017

Journal of Geometry and Physics

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Abstract. By studying the development of shock waves out of discontinuity waves, in 1954 P. Lax discovered a class of PDEs, which he called "completely exceptional", where such a transition does not occur after a finite time. A straightforward integration of the completely exceptionality conditions allowed Boillat to show that such PDEs are actually of Monge-Ampère type. In this paper, we first recast these conditions in terms of characteristics, and then we show that the completely exceptional PDEs, with 2 or 3 independent variables, can be described in terms of the conformal geometry of the Lagrangian Grassmannian, where they are naturally embedded. Moreover, for an arbitrary number of independent variables, we show that the space of r th degree sections of the Lagrangian Grassmannian can be resolved via a BGG operator. In the particular case of 1 st degree sections, i.e., hyperplane sections or, equivalently, Monge-Ampère equations, such operator is a close analog of the trace-free second fundamental form.

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Recent Results on Wave Propagation in Continuum Models

Cited by 4 publications

References 27 publications

Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas

Similarity Solutions and Strong Shocks in Extended Thermodynamics of Rarefied Gas

Early history of extended irreversible thermodynamics (1953–1983): An exploration beyond local equilibrium and classical transport theory

Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution

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