  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.
