A Comparative Study of 3d Cumulant and Central Moments Lattice Boltzmann Schemes with Interpolated Boundary Conditions for the Simulation of Thermal flows in High Prandtl Number Regime

• DOI: 10.2139/ssrn.4080592
• Publication Date: 2022-04-12T04:49:09Z
• Authors: Grzegorz Marcin G...; Łukasz Łaniewski-...
• Keywords: Cumulant; Lattice Boltzmann methods; Lattice (music)

Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity obey Courant–Friedrichs–Lewy condition, numerical diffusion scheme has to be reduced. As a consequence, artefacts dominated dispersion errors commonly known wiggles. In this study, we explore possible remedies these issues in framework lattice Boltzmann method means applying novel collision kernels, lattices with large discrete velocities, namely D3Q27, second-order boundary conditions.For first time, cumulant-based operator, is utilised simulate both hydrodynamic field. Alternatively, advected field computed using central moments' operator. Different relaxation strategies have been examined additional degrees freedom introduced higher order lattice.To validate proposed kernels pure advection-diffusion problem, simulations compared against analytical solution Gaussian hill. The structure shown simulating advection square indicator function. Next, influence interpolated conditions on quality results measured case conduction between two concentric cylinders. Finally, study steady forced convection from confined cylinder performed Finite Element Method solution.It found, that must adjusted profit larger like D3Q27. Obtained show clearly it not sufficient assume only first-order moments/cumulants contribute solving macroscopic equation. moments, beneficial effect approach presented.