Shift-periodic boundary condition for heat transfer computations in lattice Boltzmann method *

With the developments in computational techniques, detailed simulations of flow thermomechanics and other phenomena in complex geometries, such as granular or porous media, are attracting increasing interest. Recently, the lattice Boltzmann method (LBM) is more and more often applied for such computations. In this work, we present a novel numerical scheme of shift-periodic boundary conditions for the internal energy distribution function in thermal LBM. As validation cases, we consider flow past an array of heated obstacles in regular and random arrangements, akin to the granular media geometry. The quality of the proposed shift-periodic scheme is documented and the LBM results are presented for temperature profiles. The developments proposed here are also of interest for volume-averaged modeling of porous media heat transfer.