  We propose a novel multi-domain grid refinement technique with extensions to
entropic incompressible, thermal and compressible lattice Boltzmann models. Its
validity and accuracy are accessed by comparison to available direct numerical
simulation and experiment for the simulation of isothermal, thermal and viscous
supersonic flow. In particular, we investigate the advantages of grid
refinement for the set-ups of turbulent channel flow, flow past a sphere,
Rayleigh-Benard convection as well as the supersonic flow around an airfoil.
Special attention is payed to analyzing the adaptive features of entropic
lattice Boltzmann models for multi-grid simulations.
