TY - JOUR

T1 - Fast spectral solution of the generalised Enskog equation for dense gases

AU - Wu, Lei

AU - Zhang, Yonghao

AU - Reese, Jason M.

PY - 2015/12/15

Y1 - 2015/12/15

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.

KW - Enskog equation

KW - dense granular gas

KW - fast spectral method

KW - rarefied gas dynamics

UR - http://www.sciencedirect.com/science/journal/00219991

U2 - 10.1016/j.jcp.2015.09.034

DO - 10.1016/j.jcp.2015.09.034

M3 - Article

VL - 303

SP - 66

EP - 79

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -