Analysis on the force evaluation by the momentum exchange method and a localized refilling scheme for the lattice Boltzmann method

Abstract

The momentum exchange method (MEM) is widely used to calculate hydrodynamic forces on solid particles in the lattice Boltzmann method. Although MEM achieves second-order accurate force computation on particles with appropriate bounce-back schemes, significant numerical fluctuations can occur when particle moves relative to the mesh lines. In this work, we extend the recent analysis of Dong et al. [1] from static flat walls to moving curved walls to examine the forces computed using MEM with different bounce-back schemes. This analysis reveals Galilean variance errors in the conventional MEM and identifies a primary source of force fluctuations due to the time-dependent distance between boundary nodes and the solid surface. Inspired by these findings, we propose a localized “refilling” scheme to initialize distribution functions on newly uncovered fluid nodes as solid objects move. Unlike existing refilling schemes, this local scheme requires no information from neighboring nodes, making it easier to implement and reducing data communication load in parallel computing. The force fluctuations with this new scheme are also significantly lower than those with existing alternatives.