  In most current debris disc models, the dynamical and the collisional
evolutions are studied separately, with N-body and statistical codes,
respectively, because of stringent computational constraints. We present here
LIDT-DD, the first code able to mix both approaches in a fully self-consistent
way. Our aim is for it to be generic enough so as to be applied to any
astrophysical cases where we expect dynamics and collisions to be deeply
interlocked with one another: planets in discs, violent massive breakups,
destabilized planetesimal belts, exozodiacal discs, etc. The code takes its
basic architecture from the LIDT3D algorithm developed by Charnoz et al.(2012)
for protoplanetary discs, but has been strongly modified and updated in order
to handle the very constraining specificities of debris discs physics:
high-velocity fragmenting collisions, radiation-pressure affected orbits,
absence of gas, etc. In LIDT-DD, grains of a given size at a given location in
a disc are grouped into "super-particles", whose orbits are evolved with an
N-body code and whose mutual collisions are individually tracked and treated
using a particle-in-a-box prescription. To cope with the wide range of possible
dynamics, tracers are sorted and regrouped into dynamical families depending on
their orbits. The code retrieves the classical features known for debris discs,
such as the particle size distributions in unperturbed discs, the outer radial
density profiles (slope in -1.5) outside narrow collisionally active rings, and
the depletion of small grains in "dynamically cold" discs. The potential of the
new code is illustrated with the test case of the violent breakup of a massive
planetesimal within a debris disc. The main potential future applications of
the code are planet/disc interactions, and more generally any configurations
where dynamics and collisions are expected to be intricately connected.
