  In this paper, we provide a systematic analysis of some finite volume lattice
Boltzmann schemes in two dimensions. A complete iteration cycle in time
evolution of discretized distribution functions is formally divided into
collision and propagation (streaming) steps. Considering mass and momentum
conserving properties of the collision step, it becomes obvious that changes in
the momentum of finite volume cells is just due to the propagation step.
Details of the propagation step are discussed for different approximate schemes
for the evaluation of fluxes at the boundaries of the finite volume cells.
Moreover, a full Chapman-Enskog analysis is conducted allowing to recover the
Navier-Stokes equation. As an important result of this analysis, the relation
between the lattice Boltzmann relaxation time and the kinematic viscosity of
the fluid is derived for each approximate flux evaluation scheme. In
particular, it is found that the constant upwind scheme leads to a positive
numerical viscosity while the central scheme as well as the linear upwind
scheme are free of this artifact.

Fluid Dynamics;Mesoscale and Nanoscale Physics;Computational Physics