Fast spectral solution of the generalised Enskog equation for dense gases

Lei Wu, Yonghao Zhang, Jason M. Reese

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient.
LanguageEnglish
Pages66-79
Number of pages12
JournalJournal of Computational Physics
Volume303
Early online date28 Sep 2015
DOIs
Publication statusPublished - 15 Dec 2015

Fingerprint

spectral methods
Gases
gases
costs
Couette flow
inelastic collisions
Velocity distribution
laminar flow
temperature profiles
Distribution functions
Molecular dynamics
Costs
elastic scattering
velocity distribution
distribution functions
molecular dynamics
operators
collisions
coefficients
simulation

Keywords

  • Enskog equation
  • dense granular gas
  • fast spectral method
  • rarefied gas dynamics

Cite this

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title = "Fast spectral solution of the generalised Enskog equation for dense gases",
abstract = "We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient.",
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Fast spectral solution of the generalised Enskog equation for dense gases. / Wu, Lei; Zhang, Yonghao; Reese, Jason M.

In: Journal of Computational Physics, Vol. 303, 15.12.2015, p. 66-79.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Wu, Lei

AU - Zhang, Yonghao

AU - Reese, Jason M.

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N2 - We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient.

AB - We propose a fast spectral method for solving the generalized Enskog equation for dense gases. For elastic collisions, the method solves the Enskog collision operator with a computational cost of O(Md-1Nd logN), where d is the dimension of the velocity space, and Md-1 and Nd are the number of solid angle and velocity space discretizations, respectively. For inelastic collisions, the cost is N times higher. The accuracy of this fast spectral method is assessed by comparing our numerical results with analytical solutions of the spatially homogeneous relaxation of heated granular gases. We also compare our results for force driven Poiseuille flow and Fourier flow with those from molecular dynamics and Monte Carlo simulations. Although it is phenomenological, the generalized Enskog equation is capable of capturing the flow dynamics of dense granular gases, and the fast spectral method is accurate and efficient. As example applications, Fourier and Couette flows of a dense granular gas are investigated. In additional to the temperature profile, both the density and the high-energy tails in the velocity distribution functions are found to be strongly influenced by the restitution coefficient.

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