  The double distribution function approach is an efficient route towards
extension of kinetic solvers to compressible flows. With a number of
realizations available, an overview and comparative study in the context of
high speed compressible flows is presented. We discuss the different variants
of the energy partition, analyses of hydrodynamic limits and a numerical study
of accuracy and performance with the particles on demand realization. Out of
three considered energy partition strategies, it is shown that the
non-translational energy split requires a higher-order quadrature for proper
recovery of the Navier--Stokes--Fourier equations. The internal energy split on
the other hand, while recovering the correct hydrodynamic limit with
fourth-order quadrature, comes with a non-local --both in space and time--
source term which contributes to higher computational cost and memory overhead.
Based on our analysis, the total energy split demonstrates the optimal overall
performance.
