  Thermal flows characterized by high Prandtl number are numerically
challenging as the transfer of momentum and heat occurs at different time
scales. To account for very low thermal conductivity and obey the
Courant-Friedrichs-Lewy condition, the numerical diffusion of the scheme has to
be reduced. As a consequence, the numerical artefacts are dominated by
dispersion errors commonly known as wiggles. In this study, we explore possible
remedies in the framework of the lattice Boltzmann method by applying novel
collision kernels, lattices with a large number of discrete velocities, namely
D3Q27, and second-order boundary conditions. For the first time, the
cumulant-based collision operator is utilised to simulate both the hydrodynamic
and the thermal field. Alternatively, the advected field is computed using the
central moments' collision operator. Different relaxation strategies have been
examined to account for additional degrees of freedom introduced by a
higher-order lattice. To validate the proposed kernels for a pure
advection-diffusion problem, the numerical simulations are compared against an
analytical solution of a Gaussian hill. The structure of the numerical
dispersion is shown by simulating advection and diffusion of a square indicator
function. Finally, a study of steady forced heat convection from a confined
cylinder is performed and compared against a FEM solution. Numerical results
confirm that the relaxation scheme of the advected field must be adjusted to
profit from lattice with a larger number of discrete velocities. In all of the
performed benchmarks, the beneficial effect of the two relaxation time approach
has been shown to be superior or at least as good as counter-candidating
kernels.
