  The cosmic-ray spectrum up to the knee ($E\sim 10^{15}$ eV) is attributed to
acceleration processes taking place at the blastwaves which bound supernova
remnants. Theoretical predictions give a similar estimate for the maximum
energy which can be reached at supernova remnant shocks by particle
acceleration. Electrons with energies of the order $\sim 10^{15}$ eV should
give a nonthermal X-ray component in young supernova remnants. Recent
observations of SN1006 and G347.3-0.5 confirm this prediction. We present a
method which uses hydrodynamical simulations to describe the evolution of a
young remnant. These results are combined with an algorithm which
simultaneously calculates the associated particle acceleration. We use the test
particle approximation, which means that the back-reaction on the dynamics of
the remnant by the energetic particles is neglected. We present synchrotron
maps in the X-ray domain, and present spectra of the energies of the electrons
in the supernova remnant. Some of our results can be compared directly with
earlier semi-analytical work on this subject by Reynolds [1].
