  A numerical hydrodynamic model of a vibrated granular bed in 2D is elaborated
based on a highly accurate Shock Capturing scheme applied to the compressible
Navier-Stokes equations for granular flow. The hydrodynamic simulation of
granular flows is numerically difficult, particularly in systems where dilute
and dense regions occur at the same time and interact with each other. As an
example of such a problematic system we investigate the formation of Faraday
waves in a 2d system which is exposed to vertical vibration in the presence of
gravity. The results of the CHD agree quantitatively well with event-driven
Molecular Dynamics.
