  In the last decade, ground-based Imaging Atmospheric Cherenkov Telescopes
have discovered about 175 very-high-energy (VHE; $E >$ 100 GeV) gamma-ray
sources, with more to follow with the development of H.E.S.S. II and CTA.
Nearly 40 of these are confirmed pulsar wind nebulae (PWNe). We present results
from a leptonic emission code that models the spectral energy density of a PWN
by solving a Fokker-Planck-type transport equation and calculating inverse
Compton and synchrotron emissivities. Although models such as these have been
developed before, most of them model the geometry of a PWN as that of a single
sphere. We have created a time-dependent, multi-zone model to investigate
changes in the particle spectrum as the particles traverse through the PWN, by
considering a time and spatially-dependent magnetic field, spatially-dependent
bulk particle motion causing convection, diffusion, and energy losses (SR, IC
and adiabatic). Our code predicts the radiation spectrum at different positions
in the nebula, yielding novel results, e.g., the surface brightness versus the
radius and the PWN size as function of energy. We calibrated our new model
against more basic models using the observed spectrum of PWN G0.9+0.1,
incorporating data from H.E.S.S. as well as radio and X-ray experiments. We fit
our predicted radiation spectra to data from G21.5$-$0.9, G54.1+0.3, and HESS
J1356$-$645 and found that our model yields reasonable results for young PWNe.
We next performed a parameter study which gave significant insight into the
behaviour of the PWN for different scenarios. Our model is now ready to be
applied to a population of PWNe to probe possible trends such as the surface
brightness as a function of spin-down of the pulsar.
