Supernova remnants are efficient particle accelerators. In their blast
waves, electrons and protons are thought to be accelerated by the
diffusive shock acceleration mechanism to energies of 10^15 eV.
We adapted an MHD code (AMRVAC) to include particle acceleration. We
are using stochastic differential equations to calculate their
time-dependent distribution function in the test-particle approach.
With this code, we simultaneously calculate the evolution of the
supernova remnant and the particle spectrum. This allows us to obtain
detailed information on the dependence of the spectrum on e.g. time,
the topology of the magnetic field, the location within the remnant,
and the equation of state. I will present our most recent results.