A Dirichlet boundary condition for the thermal lattice Boltzmann method

In this work we introduce a boundary condition for thermal lattice Boltzmann simulations that contain a Dirichlet boundary condition by bouncing back the non-equilibrium distribution of the energy distribution function. To this end the thermal lattice Boltzmann equation is modified by introducing an additional collision term that takes into account the thermal diffusivity and local solid volume fraction of a lattice (partially) covered by the solid phase. Asymptotic analysis of the boundary condition confirms that it is of second order accuracy. The method is validated using (i) an analytical solution for the Nusselt number correlation of a single sphere in an unbounded stationary fluid and (ii) direct numerical simulations of the heat transfer between a fluid and individual particles. (C) 2019 Elsevier Ltd. All rights reserved.