  We develop a multicomponent lattice Boltzmann (LB) model for the 2D
Rayleigh--Taylor turbulence with a Shan-Chen pseudopotential implemented on
GPUs. In the immiscible case this method is able to accurately overcome the
inherent numerical complexity caused by the complicated structure of the
interface that appears in the fully developed turbulent regime. Accuracy of the
LB model is tested both for early and late stages of instability. For the
developed turbulent motion we analyze the balance between different terms
describing variations of the kinetic and potential energies. Then, we analyze
the role of interface in the energy balance, and also the effects of the
vorticity induced by the interface in the energy dissipation. Statistical
properties are compared for miscible and immiscible flows. Our results can also
be considered as a first validation step to extend the application of LB model
to 3D immiscible Rayleigh-Taylor turbulence.
