Singular forces and point-like colloids in lattice Boltzmann hydrodynamics

TL;DR

This paper introduces a second-order accurate lattice Boltzmann method to incorporate arbitrary force densities, including singular forces, validated with examples and a minimal sedimenting particle model for improved computational efficiency.

Contribution

The paper presents a novel second-order accurate approach to include arbitrary force distributions, including singular forces, in lattice Boltzmann hydrodynamics.

Findings

Excellent agreement with analytical results for point forces

Validated method with multiple examples

Proposed minimal model for dilute sedimenting particles

Abstract

We present a second-order accurate method to include arbitrary distributions of force densities in the lattice Boltzmann formulation of hydrodynamics. Our method may be used to represent singular force densities arising either from momentum-conserving internal forces or from external forces which do not conserve momentum. We validate our method with several examples involving point forces and find excellent agreement with analytical results. A minimal model for dilute sedimenting particles is presented using the method which promises a substantial gain in computational efficiency.