The French neutron scattering community is proposing to build a new High-Current Accelerator-driven Neutron Source (HiCANS). Such a source would use a low-energy proton accelerator, a few tens of MeV, to produce thermal and cold neutrons and power an instrumental suite of around ten spectrometers. The aim of the thesis project is to build a multi-scale description of the operation of a neutron scattering spectrometer, ranging from the description of microscopic neutron moderation processes and neutron interactions with atomic structure and sample dynamics, to the propagation of neutrons through advanced optical elements and the production of background by secondary particles. The ultimate aim is to be able to carry out virtual neutron scattering experiments and accurately predict instruments performances on the future ICONE source.