An accurate lattice Boltzmann method for interface capturing

TL;DR

This paper introduces a highly accurate lattice Boltzmann method for interface capturing in multiphase flows, based on a modified Allen-Cahn equation that conserves mass and improves numerical precision at small interface scales.

Contribution

The paper presents a novel lattice Boltzmann approach utilizing a modified Allen-Cahn equation with a carefully incorporated forcing term for improved interface accuracy.

Findings

More numerically accurate than existing models at small interface thickness

Successfully simulates interface-tracking with high precision

Maintains mass conservation in the interface-capturing process

Abstract

Accurately solving phase interface plays a great role in modeling immiscible multiphase flow system. In this letter, we propose an accurate interface-capturing lattice Boltzmann method from the perspective of the modified Allen-Cahn equation (ACE). The modified ACE is built based on the commonly used conservative formulation via the relation between the signed-distance function and the order parameter also maintaining the mass-conserved characteristic. A suitable forcing term is carefully incorporated into the lattice Boltzmann equation for correctly recovering the target equation. We then test the proposed method by simulating a typical interface-tracking problem of single vortex and demonstrate that the present model can be more numerically accurate than the existing lattice Boltzmann models for the conservative ACE, especially at a small interface-thickness scale.