Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow

Abstract

In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning moving rigid solid particles suspended a viscous fluid. Three aspects relevant to the interaction between flow of a viscous fluid and moving solid boundaries are considered. First, the popular interpolated bounce back scheme is examined both theoretically and numerically. It is important to recognize that even though significant efforts had previously been devoted to the performance, especially the accuracy, of different interpolated bounce back schemes for a fixed boundary, there were relatively few studies focusing on moving solid surfaces. In this study, different interpolated bounce back schemes are compared theoretically for a moving boundary. Then, several benchmark cases are presented to show their actual performance in numerical simulations. Second, we examine different implementations of the momentum exchange method to calculate hydrodynamic force and torque acting on a moving surface. The momentum exchange method is well established for fixed solid boundaries, however, for moving solid boundaries there are still open issues such as unphysical force fluctuations and Galilean invariance errors. Recent progress in this direction is discussed, along with our own interpretations and modifications. Several benchmark cases, including a particle-laden turbulent channel flow, are used to demonstrate the effects of different modifications on the accuracy and physical results under different physical configurations. The third aspect is the refilling scheme for constructing the unknown distribution functions for the new fluid nodes that emerge from the previous solid region as a particle moves relative to a fixed lattice grid. We examine and compare the performance of the refilling schemes introduced by Fang et al. (2002), Lallemand and Luo (2003), and Caiazzo (2008). We demonstrate that improvements can be made to suppress force fluctuations resulting from refilling.