  We present a 3-dimensional model of supernova remnants (SNRs) where the
hydrodynamical evolution of the remnant is modeled consistently with nonlinear
diffusive shock acceleration occuring at the outer blast wave. The model
includes particle escape and diffusion outside of the forward shock, and
particle interactions with arbitrary distributions of external ambient
material, such as molecular clouds. We include synchrotron emission and
cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton
(IC), and Coulomb energy-loss. Boardband spectra have been calculated for
typical parameters including dense regions of gas external to a 1000 year old
SNR. In this paper, we describe the details of our model but do not attempt a
detailed fit to any specific remnant. We also do not include magnetic field
amplification (MFA), even though this effect may be important in some young
remnants. In this first presentation of the model we don't attempt a detailed
fit to any specific remnant. Our aim is to develop a flexible platform, which
can be generalized to include effects such as MFA, and which can be easily
adapted to various SNR environments, including Type Ia SNRs, which explode in a
constant density medium, and Type II SNRs, which explode in a pre-supernova
wind. When applied to a specific SNR, our model will predict cosmic-ray spectra
and multi-wavelength morphology in projected images for instruments with
varying spatial and spectral resolutions. We show examples of these spectra and
images and emphasize the importance of measurements in the hard X-ray, GeV, and
TeV gamma-ray bands for investigating key ingredients in the acceleration
mechanism, and for deducing whether or not TeV emission is produced by IC from
electrons or neutral pions from protons.
