  We consider the Gross-Pitaevskii equation with a confining ring potential
with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we
numerically highlight the nucleation of quantum vortices in a particular regime
throughout the dynamics. Numerical computations are made via a Strang splitting
time integration and a two-point flux approximation Finite Volume scheme based
on a particular admissible triangulation. We also develop numerical algorithms
for vortex tracking adapted to our finite volume framework.
