Characteristic boundary condition for thermal lattice Boltzmann methods

We introduce a non-reflecting boundary condition for the simulation of thermal flows with the lattice Boltzmann Method (LBM). We base the derivation on the locally one-dimensional inviscid analysis, and define target macroscopic values at the boundary aiming at minimizing the effect of reflections of outgoing waves on the bulk dynamics. The resulting macroscopic target values are then enforced in the LBM using a mesoscopic Dirichlet boundary condition. We present a procedure which allows to implement the boundary treatment for both single-speed and high order multi-speed LBM models, by conducting a layerwise characteristic analysis. We demonstrate the effectiveness of our approach by providing qualitative and quantitative comparison of several strategies for the implementation of a open boundary condition in standard numerical benchmarks. We show that our approach allows to achieve increasingly high accuracy by relaxing transversal and viscous terms towards prescribed target values.