  The Vicsek model is a very popular individual based model which describes
collective behavior among animal societies. A macroscopic version of the Vicsek
model has been derived from a large scale limit of this individual based model
\cite{degond2007ml}. In this work, we want to numerically validate this
Macroscopic Vicsek model (MV). To this aim, we compare the simulations of the
macroscopic and microscopic models one with each other. The MV model is a
non-conservative hyperbolic equation with a geometric constraint. Due to the
lack of theory for this kind of equations, we derive several equivalents for
this system leading to specific numerical schemes. The numerical simulations
reveal that the microscopic and macroscopic models are in good agreement
provided that we choose one of the proposed formulations based on a relaxation
of the geometric constraint. This confirms the relevance of the macroscopic
equation but it also calls for a better theoretical understanding of this type
of equations.
