Derivation of transient relativistic fluid dynamics from the Boltzmann equation

By G. Denicol, H. Niemi, E. Molnár, Dirk H. Rischke. 2012

412 citations recorded by the source corpus.

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients c information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion. PACS numbers:

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ffb55ae4799600595ece1cc7e35c8afe2ab12a7a

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In Applied Mathematics

1. A. Jaiswal
2. P. Braun-Munzinger
3. Chun Shen
4. V. Koch
5. T. Schaefer
6. V. Roy
7. J. Stachel
8. Li Yan

In Atomic and Molecular Physics, and Optics

1. V. Koch
2. T. Schaefer
3. P. Braun-Munzinger
4. J. Stachel
5. P. Kovtun
6. A. Jaiswal
7. Chun Shen
8. V. Roy

In Nuclear and High Energy Physics

1. T. Schaefer
2. V. Koch
3. J. Stachel
4. P. Braun-Munzinger
5. P. Kovtun
6. Chun Shen
7. Li Yan
8. A. Jaiswal

Citations in the corpus

• Properties of hot and dense matter from relativistic heavy ion collisions (2015, background): “(25) can also be obtained in kinetic theory [162,163], but in this case certain terms allowed by the symmetries, like the 3-term in Eq.”
• Relativistic Hydrodynamics in Heavy-Ion Collisions: General Aspects and Recent Developments (2016, methodology): “For a system of massless particles, the kinetic theory results for second-order transport coefficients agree in the case of both moment method [58] as well as the the Chapman-Enskog like iterative solution of the Boltzmann equation [66].”
• Recent development of hydrodynamic modeling in heavy-ion collisions (2020, methodology): “For instance, it can also be formulated according to the DNMR approach as [49] p ¼ 4 3 g s sp dp ds þ bp p s vs 2 p g p2 s ; ð21Þ where bp and v are the transport coefficients in this alternate formulation.”
• First-order relativistic hydrodynamics is stable (2019, methodology): “This is what is done in the Israel-Stewart theory [6, 7], and in more modern derivations of the analogous stable and causal hydrodynamics such as [8, 9, 10].”
• Relativistic Fluid Dynamics in and out of Equilibrium (2017, neutral): “R = 0), but chose to go beyond second-order accuracy by distinguishing between terms such as ζπ∇λ u and ησΠ [142].”