  In this contribution we study the formal ability of a multi-resolution-times
lattice Boltzmann scheme to approximate isothermal and thermal compressible
Navier Stokes equations with a single particle distribution. More precisely, we
consider a total of 12 classical square lattice Boltzmann schemes with
prescribed sets of conserved and nonconserved moments. The question is to
determine the algebraic expressions of the equilibrium functions for the
nonconserved moments and the relaxation parameters associated to each scheme.
We compare the fluid equations and the result of the Taylor expansion method at
second order accuracy for bidimensional examples with a maximum of 17
velocities and three-dimensional schemes with at most 33 velocities. In some
cases, it is not possible to fit exactly the physical model. For several
examples, we adjust the Navier Stokes equations and propose nontrivial
expressions for the equilibria.
