Improved third-order scheme in pseudopotential lattice Boltzmann model for multiphase flows

TL;DR

This paper introduces an improved third-order scheme for pseudopotential lattice Boltzmann models that effectively suppresses spurious velocity oscillations in multiphase flow simulations, enhancing accuracy without added complexity.

Contribution

The authors propose a new third-order scheme based on discrete analysis that reduces spurious velocities in multiphase LB simulations without increasing computational cost.

Findings

The improved scheme effectively suppresses spurious velocity oscillations near phase interfaces.

Numerical tests confirm the scheme's effectiveness in various flow scenarios.

The scheme maintains original computational complexity and accuracy in static conditions.

Abstract

The lattice Boltzmann (LB) equation with a third-order scheme can be regarded as a unified and self-consistent framework of the pseudopotential LB model for multiphase flows. In this work, we theoretically analyze pseudopotential LB simulations of two-phase Poiseuille flow at the discrete level. The finite-difference velocity equation is derived for both grid-aligned and grid-oblique cases. The terms responsible for spurious velocity oscillations near the phase interface are identified. Based on this discrete-level analysis, an improved third-order scheme is proposed to suppress spurious velocity oscillations. This scheme does not introduce any additional conceptual or computational complexity compared with the original one and reduces to the original scheme under static conditions. Numerical simulations of two-phase Poiseuille flow validate the present theoretical analysis and demonstrate the effectiveness of the improved scheme. Then, annular shear flow with a curved phase interface is considered to show that spurious velocity oscillations can also be effectively suppressed by the improved scheme in cases with such interfaces. Finally, the falling of a droplet in a vertical channel is simulated, and the results show that spurious velocity oscillations can lead to an overestimation of the drag force and distinct falling patterns. These results highlight the necessity of using the improved third-order scheme to suppress spurious oscillations and obtain reliable results.