A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method

TL;DR

This paper introduces a unified, second-order accurate operator splitting framework for fluid-particle coupling in the lattice Boltzmann method, improving accuracy and stability in multi-scale fluid simulations.

Contribution

It develops a unified, second-order time-accurate scheme for coupling immersed solids to lattice Boltzmann fluids, unifying various methods under a common framework.

Findings

Derived second-order schemes for immersed boundary and force coupling.

Introduced a modified external boundary force for better no-slip accuracy.

Enhanced long-term stability in multi-scale fluid-particle simulations.

Abstract

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.