  In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is
developed in combination with the double-distribution-function (DDF) approach.
A density distribution function relaxed by the cascaded scheme is employed to
solve the flow field, and a total energy distribution function relaxed by the
BGK scheme is used to solve temperature field, where two distribution functions
are coupled naturally. The forcing terms are incorporated by means of central
moments, which is consistent with the previous force scheme [Premnath \emph{et
al.}, Phys. Rev. E \textbf{80}, 036702 (2009)] but the derivation is more
intelligible and the evolution process is simpler. In the method, the viscous
heat dissipation and compression work are taken into account, the Prandtl
number and specific-heat ratio are adjustable, the external force is considered
directly without the Boussinesq assumption, and the low-Mach number
compressible flows can also be simulated. The forcing scheme is tested by
simulating a steady Taylor-Green flow, and the new TCLBM is then tested by
numerical experiments of the thermal Couette flow, low-Mach number shock tube
problem, and Rayleigh-B\'{e}nard convection. The simulation results agree well
with the analytical solutions and/or results given by previous researchers.
