Comparison of boundary treatments in thermal Lattice Boltzmann simulations of moving particles in fluids

Various numerical schemes have been developed in recent years to simulate particle-laden flows. The Lattice Boltzmann method (LBM) has emerged as an efficient tool for direct numerical simulations in which the flow field around the particles can be fully resolved. In the thermal Lattice Boltzmann method not only the flow field but also the temperature field is calculated by using one distribution function for the fluid density and one for the fluid temperature. The treatment of curved solid-fluid boundaries is crucial for the simulation of particulate flows with this method. While several aspects of moving boundaries have been discussed in previous studies for the non-thermal LBM, it remains unknown to what extend these findings are transferable to the thermal LBM. In this work, we consider a 3D thermal LBM with a multiple-relaxation-time (MRT) collision operator and compare different techniques that can be applied to handle the moving boundary.
There are three key aspects in the LBM that need to be considered at the boundary: the momentum exchange method calculating the drag force acting upon particles, the bounce-back scheme determining the bounce-back of density distribution functions at a boundary, and the refilling algorithm assigning a value to the unknown density distribution functions at lattice nodes uncovered by the particle. First, we demonstrate how the choice of the technique to address these problems in the flow field impacts the results for the temperature field in the thermal LBM. In a second step, we focus on the thermal side where similar techniques need to be applied. We compare different refilling strategies and bounce-back schemes for the temperature distribution functions and assess heat transfer calculation methods for the particle surface.
The performance of these implementations is evaluated by comparing the simulation results in terms of accuracy and stability for a moving particle in a channel flow with a Galilean invariant reference system in which the particle’s position is fixed. We conduct this analysis for various Reynolds and Prandtl numbers to test the applicability of the individual techniques to varying flow conditions. Moreover, we demonstrate the potential of the implementation found to be superior by considering a more complex flow field in a particle packing. Our findings serve as a guideline for choosing suitable moving boundary treatments in thermal LBM simulations of particle-laden flows.