  We present a thorough investigation of the particles on demand kinetic model.
After a brief introduction of the method, an appropriate multiscale analysis is
carried out to derive the hydrodynamic limit of the model. In this analysis,
the effect of the time-space dependent comoving reference frames are taken into
account. This could be regarded as a generalization of the conventional
Chapman-Enskog analysis applied to the lattice Boltzmann models which feature
global constant reference frames. Further simulations of target benchmarks
provide numerical evidence confirming the theoretical predictions.
