  We present results of a high resolution numerical study of two dimensional
(2d) Rayleigh-Taylor turbulence using a recently proposed thermal lattice
Boltzmann method (LBT). The goal of our study is both methodological and
physical. We assess merits and limitations concerning small- and large-scale
resolution/accuracy of the adopted integration scheme. We discuss
quantitatively the requirements needed to keep the method stable and precise
enough to simulate stratified and unstratified flows driven by thermal active
fluctuations at high Rayleigh and high Reynolds numbers. We present data with
spatial resolution up to 4096 x 10000 grid points and Rayleigh number up to Ra
~ 10^11 . The statistical quality of the data allows us to investigate velocity
and temperature fluctuations, scale-by-scale, over roughly four decades. We
present a detailed quantitative analysis of scaling laws in the viscous,
inertial and integral range, supporting the existence of a Bolgiano-like
inertial scaling, as expected in 2d systems. We also discuss the presence of
small/large intermittent deviation to the scaling of velocity/temperature
fluctuations and the Rayleigh dependency of gradients flatness.
