Density gradient calculation in a class of multiphase lattice Boltzmann models

Rongzong Huang; Huiying Wu; Nikolaus A Adams

doi:10.1103/PhysRevE.100.043306

Density gradient calculation in a class of multiphase lattice Boltzmann models

Phys Rev E. 2019 Oct;100(4-1):043306. doi: 10.1103/PhysRevE.100.043306.

Authors

Rongzong Huang^{1

2

3}, Huiying Wu², Nikolaus A Adams³

Affiliations

¹ School of Energy Science and Engineering, Central South University, 410083 Changsha, China.
² School of Mechanical Engineering, Shanghai Jiao Tong University, 200240 Shanghai, China.
³ Institute of Aerodynamics and Fluid Mechanics, Technical University of Munich, 85748 Garching, Germany.

PMID: 31771029
DOI: 10.1103/PhysRevE.100.043306

Abstract

The multiphase lattice Boltzmann (LB) models based on pairwise interactions show great potential for simulating multiphase flows due to the conceptual and computational simplicity. Although the dynamics of multiphase flows are reproduced by the pairwise interaction force, the gradient of density (or effective density, i.e., pseudopotential) is implicitly involved in these models via the specialized forcing scheme or the consistent scheme for ɛ^{3}-order term. This work focuses on the calculation of density gradient in this class of multiphase LB models. Theoretical analyses are first carried out to reveal the involvement and calculation of density gradient. On the basis of a low Mach number approximation, an improved scheme is then proposed to calculate the density gradient for the recent LB model with self-tuning equation of state. Analytical and numerical calculations show that the improved scheme is more accurate and can help to reduce the numerical error when the reduced temperature is relatively low.