Stability analysis for a thermodynamically consistent model of relativistic fluid dynamics

Stricker, Laura; Öttinger, Hans Christian

doi:10.1103/physreve.99.013105

Cited by 11 publications

(39 citation statements)

References 33 publications

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“…As it was shown in [8], non-relativistic SHTC equations can be viewed as a particular realization of the GENERIC formulation for non-equilibrium thermodynamics. It is, therefore, not surprising that the same heat conduction equations were also proposed by Öttinger [59][60][61] within the GENERIC approach in the relativistic context.…”

Section: (C) Heat Conductionmentioning

confidence: 54%

“…The irreversible part is represented by algebraic (no space and time derivatives) relaxation-type source terms and can be viewed as gradients of a dissipation potential intimately connected with the entropy, see [4]. We have observed that our variational formulation of the relativistic heat conduction is equivalent to the Hamiltonian formulation by Öttinger [34,32] within the GENERIC approach. The viscous part which is governed by the distortion evolution equation (40b) is different from that presented in [34,32].…”

Section: Numerical Examplesmentioning

confidence: 95%

“…We have observed that our variational formulation of the relativistic heat conduction is equivalent to the Hamiltonian formulation by Öttinger [34,32] within the GENERIC approach. The viscous part which is governed by the distortion evolution equation (40b) is different from that presented in [34,32]. Nevertheless, it also admits a Hamiltonian formulation as proven in [4].…”

Section: Numerical Examplesmentioning

confidence: 99%

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A new continuum model for general relativistic viscous heat-conducting media

Romenski

Peshkov

Dumbser

et al. 2020

Phil. Trans. R. Soc. A.

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The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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Section: (C) Heat Conductionmentioning

confidence: 54%

Section: Numerical Examplesmentioning

confidence: 95%

Section: Numerical Examplesmentioning

confidence: 99%

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A new continuum model for general relativistic viscous heat-conducting media

Romenski

Peshkov

Dumbser

et al. 2020

Phil. Trans. R. Soc. A.

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“…Recall that the classical Navier-Stokes fluid dynamics can not be applied to modeling relativistic flows due to the intrinsic causality and stability issues of the Navier-Stokes equations [88]. To fix these issues of the classical fluid dynamics, several alternatives have been developed [74,66,54,97,40,37,98] to name just a few. The geometrical nature of our theory with the underlying Riemann-Cartan geometry also suggests that it would be not difficult to obtain the relativistic version of the theory which should fit well to the geometrical settings of the general relativity or its teleparallel equivalent [1].…”

Section: Discussionmentioning

confidence: 99%

Continuum mechanics with torsion

Peshkov

Romenski

Dumbser

2019

Continuum Mech. Thermodyn.

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This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irregular dynamics of small scale vortexes, we further generalize our unified first-order hyperbolic formulation of continuum fluid and solid mechanics which treats the flowing medium as a Riemann-Cartan manifold with zero curvature but non-vanishing torsion. We associate the rotational degrees of freedom of the main field of our theory, the distortion field, to the dynamics of microscopic (unresolved) vortexes. The distortion field characterizes the deformation and rotation of the material elements and can be viewed as anholonomic basis triad with non-vanishing torsion. The torsion tensor is then used to characterize distortion's spin and is treated as an independent field with its own time evolution equation. This new governing equation has essentially the structure of the non-linear electrodynamics in a moving medium and can be viewed as a Yang-Mills-type gauge theory. The system is closed by providing an example of the total energy potential. The extended system describes not only irreversible dynamics (which raises the entropy) due to the viscosity or plasticity effect but it also has dispersive features which are due to the reversible energy exchange (which conserves the entropy) between micro and macro scales. Both the irreversible and dispersive processes are represented by relaxation-type algebraic source terms so that the overall system remains first-order hyperbolic. The turbulent state is then treated as an excitation of the equilibrium laminar state due to the non-linear interplay between dissipation and dispersion.

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“…By adding the heat flux, even nonisothermal rheology can be based on flux variables. Also the equations for relativistic hydrodynamics are usually based on flux variables [59][60][61][62][63][64][65][66] (see also article by Romenski, Peshkov, Dumbser and Fambri in this theme issue).…”

Section: Conclusion and Challengesmentioning

confidence: 99%

Formulation of moment equations for rarefied gases within two frameworks of non-equilibrium thermodynamics: RET and GENERIC

Öttinger

Struchtrup

Torrilhon

2020

Phil. Trans. R. Soc. A.

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In this work, we make a further step in bringing together different approaches to non-equilibrium thermodynamics. The structure of the moment hierarchy derived from the Boltzmann equation is at the heart of rational extended thermodynamics (RET, developed by Ingo Müller and Tommaso Ruggeri). Whereas the full moment hierarchy has the structure expressed in the general equation for the nonequilibrium reversible–irreversible coup- ling (GENERIC), the Poisson bracket structure of reversible dynamics postulated in that approach is a major obstacle for truncating moment hierarchies, which seems to work only in exceptional cases (most importantly, for the five moments associated with conservation laws). The practical importance of truncated moment hierarchies in rarefied gas dynamics and microfluidics motivates us to develop a new strategy for establishing the full GENERIC structure of truncated moment equations, based on non-entropy-producing irreversible processes associated with Casimir symmetry. Detailed results are given for the special case of 10 moments. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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Stability analysis for a thermodynamically consistent model of relativistic fluid dynamics

Cited by 11 publications

References 33 publications

A new continuum model for general relativistic viscous heat-conducting media

A new continuum model for general relativistic viscous heat-conducting media

Continuum mechanics with torsion

Formulation of moment equations for rarefied gases within two frameworks of non-equilibrium thermodynamics: RET and GENERIC

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