  The Vicsek model (Vicsek et al. 1995) is a very popular minimalist model to
study active matter with a number of applications to biological systems at
different length scales. With its off-lattice implementation and periodic
boundary conditions, it aims at the analysis of bulk behaviour of a limited
number of particles. We introduce an efficient on-lattice implementation with
finite particle volume and analyse its behaviour for three different geometries
with reflective boundary conditions. For sufficiently fine lattices, the model
behaviour does not differ between off-lattice and on-lattice implementation.
The reflective boundary conditions introduce an alignment of the particles with
the boundary for low levels of noise. Numerical sensitivity analysis of the
swarming behaviour results in a detailed characterisation of the on-lattice
Vicsek model for confined geometries with reflective boundary conditions. In a
channel geometry, the boundary alignment causes swarms to move along the
channel. In a box, the edges act as swarm traps and the trapping shows a
discontinuous noise dependence. In a disk geometry, an ordered rotational state
arises. This state is well described by a novel order parameter. Our works
provides a foundation for future studies of Vicsek-like models with discretized
space.
