  With the aim of better understanding the numerical properties of the lattice
Boltzmann method (LBM), a general methodology is proposed to derive its
hydrodynamic limits in the discrete setting. It relies on a Taylor expansion in
the limit of low Knudsen numbers. With a single asymptotic analysis, two kinds
of deviations with the Navier-Stokes (NS) equations are explicitly evidenced:
consistency errors, inherited from the kinetic description of the LBM, and
numerical errors attributed to its space and time discretization. The
methodology is applied to the Bhatnagar-Gross-Krook (BGK), the regularized and
the multiple relaxation time (MRT) collision models in the isothermal
framework. Deviation terms are systematically confronted to linear analyses in
order to validate their expressions, interpret them and provide explanations
for their numerical properties. The low dissipation of the BGK model is then
related to a particular pattern of its error terms in the Taylor expansion.
Similarly, dissipation properties of the regularized and MRT models are
explained by a phenomenon referred to as hyperviscous degeneracy. The latter
consists in an unexpected resurgence of high-order Knudsen effects induced by a
large numerical pre-factor. It is at the origin of over-dissipation and severe
instabilities in the low-viscosity regime.
