  Gravitational waves are one of the most important diagnostic tools in the
analysis of strong-gravity dynamics and have been turned into an observational
channel with LIGO's detection of GW150914. Aside from their importance in
astrophysics, black holes and compact matter distributions have also assumed a
central role in many other branches of physics. These applications often
involve spacetimes with $D>4$ dimensions where the calculation of gravitational
waves is more involved than in the four dimensional case, but has now become
possible thanks to substantial progress in the theoretical study of general
relativity in $D>4$. Here, we develop a numerical implementation of the
formalism by Godazgar and Reall (Ref.[1]) -- based on projections of the Weyl
tensor analogous to the Newman-Penrose scalars -- that allows for the
calculation of gravitational waves in higher dimensional spacetimes with
rotational symmetry. We apply and test this method in black-hole head-on
collisions from rest in $D=6$ spacetime dimensions and find that a fraction
$(8.19\pm 0.05)\times 10^{-4}$ of the Arnowitt-Deser-Misner mass is radiated
away from the system, in excellent agreement with literature results based on
the Kodama-Ishibashi perturbation technique. The method presented here
complements the perturbative approach by automatically including contributions
from all multipoles rather than computing the energy content of individual
multipoles.
