Session: 09-03: Computational Methods in Micro/ Nanoscale Transport

Paper Number: 132741

132741 - Numerical Modelling of Molecular Attraction Force in Shakov-Enskog-Vlasov Equation 

Abstract: 

Numerical Modelling of Molecular Attraction Force in Shakov-Enskog-Vlasov Equation
Zuoxu Li(1), Shaokang Li(2), and Yonghao Zhang[1,a)]
(1)Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of
Sciences, Beijing, 100190, China
(2)School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, UK
a)Corresponding author: yonghao.zhang@imech.ac.cn
Nano-scale non-equilibrium evaporation phenomena are ubiquitous in nature and industry.
Non-equilibrium flow features including velocity slip and temperature are often difficult to be
captured by continuum fluid models. Therefore, gas kinetic theory such as the Boltzmann
equation for dilute gases is commonly used to describe non-equilibrium flows. When gas-liquid
phase transition occurs, the size of the molecules is no longer negligible compared to the mean
free path of the molecules, so the molecular collisions are no longer local. To consider the
effect of molecular size, the Enskog equation was developed for dense gases, which was ex-
tended from the Boltzmann equation. However, for the gas-liquid phase transition problem,
the long-range molecular attraction forces play an important role, which is neglected in the
hard-sphere model used by the Enskog equation. This molecular attraction force may be ap-
proximated as a body force using the mean field theory. The resulting Enskog-Vlasov equation
can capture non-equilibrium phase change. But it is computationally difficult and expensive
to solve. By simplifying the Enskog collision term, we have recently developed a simplified
Shakov-Enskog-Vlasov model. However, in order to accurately capture the effect of long-range
molecular attraction forces, direct employment of finite difference method requires a signifi-
cant number of velocity points, resulting in substantial computational cost, especially in three
dimensions. In this paper, we expand the distribution function in the velocity space using
the Hermite polynomial series for the mean-field body force term. In the obtained explicit
formula for the body force term, only some macroscopic moments need to be calculated. As
the conservation of the leading-order moments can be ensured in our numerical algorithm, nu-
merical diffusion problem associated with low-speed evaporating flows may be mitigated. Our
numerical validations include simulation of the equilibrium state of gas-liquid coexistence show
that the proposed new method can achieve the same accuracy with a smaller number of the
discrete velocities than the finite difference method. For the 1-dimension case, it requires only
40 discrete points in the velocity space to accurately solve the number density profile under
equilibrium conditions, whereas the finite difference method necessitates more than 100 discrete
points. In addition, we confirm that in this new method, the Gaussian Hermite quadrature is
more accurate than the Newton-Cotes quadrature, which is expected for simulating low-speed
non-equilibrium flows.

Presenting Author: Zuoxu Li Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences

Presenting Author Biography: Zuoxu Li is a research assistant at the Institute of Mechanics, Chinese Academy of Sciences. He received a Master’s degree in mechanics from Southern University of Science and Technology, Shenzhen, China. His research interests include high-order lattice Boltzmann method and gas kinetic theory.

Authors:

Zuoxu Li Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences
Yonghao Zhang Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences
Shaokang Li The University of Edinburgh