Recent development in kinetic theory of granular materials: analysis and numerical methods

José Carrillo; Jingwei Hu; Zheng Ma; Thomas Rey

doi:10.1007/978-3-030-67104-4_1

Book Sections Year : 2021

Recent development in kinetic theory of granular materials: analysis and numerical methods

(1) , (2) , (2) , (3)

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José Carrillo

Function : Author

Department of Mathematics [Imperial College London]

Jingwei Hu

Function : Author

Department of mathematics Purdue University

Zheng Ma

Function : Author

Department of mathematics Purdue University

Thomas Rey

Function : Author
PersonId : 259
IdHAL : thomas-rey
ORCID : 0000-0001-7849-2090
IdRef : 084315431

Reliable numerical approximations of dissipative systems

Abstract

Over the past decades, kinetic description of granular materials has received a lot of attention in mathematical community and applied fields such as physics and engineering. This article aims to review recent mathematical results in kinetic granular materials, especially for those which arose since the last review by Villani on the same subject. We will discuss both theoretical and numerical developments. We will finally showcase some important open problems and conjectures by means of numerical experiments based on spectral methods.

Keywords

granular flows GPU Granular gases equation inelastic Boltzmann equation fast spectral method asymptotic behavior review hydrodynamic equations

Domains

Analysis of PDEs [math.AP] Mathematics [math]

Fichier principal

SurveyGranularGases.pdf (672.15 Ko)

figs/collisionSphere.pdf (10.51 Ko)

figs/convergence-e05-tau01-flat.pdf (20.7 Ko)

figs/convergence-e05-tau01-max.pdf (20.74 Ko)

figs/convergence-e095-tau005-max.pdf (21.04 Ko)

figs/eq-e05-tau01-flat.pdf (26.06 Ko)

figs/eq-e05-tau01-max.pdf (26.58 Ko)

figs/eq-e095-tau005-max.pdf (27.49 Ko)

figs/f_eq_tail_maxw_and_hs.pdf (17.42 Ko)

figs/figCollision.pdf (6.03 Ko)

figs/haff_var_e_02.pdf (18.44 Ko)

figs/haff_var_e_08.pdf (18.81 Ko)

figs/haff_var_gamma_heat.pdf (17.73 Ko)

figs/haff_var_gamma_no_heat.pdf (17.33 Ko)

figs/haff_var_lambda_heat.pdf (17.33 Ko)

figs/heated_Haff_cooling.pdf (18.68 Ko)

figs/heated_Haff_cooling_loglog.pdf (19.65 Ko)

figs/heated_Haff_cooling_semilogy.pdf (18.73 Ko)

figs/heated_Haff_cooling_tau.pdf (16.7 Ko)

figs/var_e_02.pdf (13.61 Ko)

figs/var_e_08.pdf (13.6 Ko)

Origin	Files produced by the author(s)

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https://hal.science/hal-02460375

Submitted on : Thursday, January 30, 2020-9:23:47 AM

Last modification on : Wednesday, November 13, 2024-4:24:11 PM

Dates and versions

hal-02460375 , version 1 (30-01-2020)

Identifiers

HAL Id : hal-02460375 , version 1
ARXIV : 2001.11206
DOI : 10.1007/978-3-030-67104-4_1

Cite

José Carrillo, Jingwei Hu, Zheng Ma, Thomas Rey. Recent development in kinetic theory of granular materials: analysis and numerical methods. Giacomo Albi; Sara Merino-Aceituno; Alessia Nota; Mattia Zanella. Trails in Kinetic Theory, Springer, pp.1-36, 2021, SEMA SIMAI Springer Series, 978-3-030-67103-7. ⟨10.1007/978-3-030-67104-4_1⟩. ⟨hal-02460375⟩

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Recent development in kinetic theory of granular materials: analysis and numerical methods

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