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Gabbana A, Simeoni D, Succi S, Tripiccione R. Probing bulk viscosity in relativistic flows. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190409. [PMID: 32564720 PMCID: PMC7333951 DOI: 10.1098/rsta.2019.0409] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/26/2020] [Indexed: 06/11/2023]
Abstract
We derive an analytical connection between kinetic relaxation rate and bulk viscosity of a relativistic fluid in d spatial dimensions, all the way from the ultra-relativistic down to the near non-relativistic regime. Our derivation is based on both Chapman-Enskog asymptotic expansion and Grad's method of moments. We validate our theoretical results against a benchmark flow, providing further evidence of the correctness of the Chapman-Enskog approach; we define the range of validity of this approach and provide evidence of mounting departures at increasing Knudsen number. Finally, we present numerical simulations of transport processes in quark-gluon plasmas, with special focus on the effects of bulk viscosity which might prove amenable to future experimental verification. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.
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Affiliation(s)
- A. Gabbana
- Università di Ferrara and INFN-Ferrara, 44122 Ferrara, Italy
- Bergische Universität Wuppertal, 42119 Wuppertal, Germany
| | - D. Simeoni
- Università di Ferrara and INFN-Ferrara, 44122 Ferrara, Italy
- Bergische Universität Wuppertal, 42119 Wuppertal, Germany
- University of Cyprus, 1678 Nicosia, Cyprus
| | - S. Succi
- Center for Life Nano Science @ La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, 00161 Roma, Italy
- Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, 00185 Roma, Italy
| | - R. Tripiccione
- Università di Ferrara and INFN-Ferrara, 44122 Ferrara, Italy
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Coreixas C, Wissocq G, Chopard B, Latt J. Impact of collision models on the physical properties and the stability of lattice Boltzmann methods. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190397. [PMID: 32564722 DOI: 10.1098/rsta.2019.0397] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/29/2020] [Indexed: 06/11/2023]
Abstract
The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.
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Affiliation(s)
- C Coreixas
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - G Wissocq
- CERFACS, 42 Avenue G. Coriolis, 31057, Toulouse Cedex, France
| | - B Chopard
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
| | - J Latt
- Department of Computer Science, University of Geneva, 1204 Geneva, Switzerland
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Gabbana A, Simeoni D, Succi S, Tripiccione R. Relativistic dissipation obeys Chapman-Enskog asymptotics: Analytical and numerical evidence as a basis for accurate kinetic simulations. Phys Rev E 2019; 99:052126. [PMID: 31212459 DOI: 10.1103/physreve.99.052126] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 11/07/2022]
Abstract
We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. We further develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison of our analytical results and numerical simulations shows that the CE method correctly captures dissipative effects, while Grad's method does not, in agreement with previous analyses performed in the (3+1)-dimensional case. These results provide a solid basis for accurately calibrated computational studies of relativistic dissipative flows.
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Affiliation(s)
- A Gabbana
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy.,Chair of Applied Mathematics and Numerical Analysis, Bergische Universität Wuppertal, D-42119 Wuppertal, Germany
| | - D Simeoni
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy.,Chair of Applied Mathematics and Numerical Analysis, Bergische Universität Wuppertal, D-42119 Wuppertal, Germany.,Department of Physics, University of Cyprus, CY-1678 Nicosia, Cyprus
| | - S Succi
- Center for Life Nano Science @ La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy.,Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, I-00185 Roma, Italy
| | - R Tripiccione
- Department of Physics and Earth Sciences, Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
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Gabbana A, Polini M, Succi S, Tripiccione R, Pellegrino FMD. Prospects for the Detection of Electronic Preturbulence in Graphene. PHYSICAL REVIEW LETTERS 2018; 121:236602. [PMID: 30576199 DOI: 10.1103/physrevlett.121.236602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Indexed: 06/09/2023]
Abstract
Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic preturbulence in graphene samples. In particular, preturbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.
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Affiliation(s)
- A Gabbana
- Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
- Bergische Universität Wuppertal, D-42119 Wuppertal, Germany
| | - M Polini
- Istituto Italiano di Tecnologia, Graphene Labs, Via Morego 30, I-16163 Genova, Italy
| | - S Succi
- Center for Life Nano Science at La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy
- Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, I-00185 Roma, Italy
| | - R Tripiccione
- Università di Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy
| | - F M D Pellegrino
- Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia 64, I-95123 Catania, Italy
- INFN, Sezione Catania, I-95123 Catania, Italy
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Gabbana A, Mendoza M, Succi S, Tripiccione R. Kinetic approach to relativistic dissipation. Phys Rev E 2017; 96:023305. [PMID: 28950626 DOI: 10.1103/physreve.96.023305] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 06/07/2023]
Abstract
Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949)0010-364010.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.
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Affiliation(s)
- A Gabbana
- INFN-Ferrara, Università di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
| | - M Mendoza
- ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Schafmattstraße 6, HIF, CH-8093 Zürich, Switzerland
| | - S Succi
- Istituto per le Applicazioni del Calcolo C.N.R., Via dei Taurini, 19, 00185 Rome, Italy and Institute for Applied Computational Science, John Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - R Tripiccione
- INFN-Ferrara, Università di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy
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