In the frame of the French trans-governmental R&D program against chemical, biological, radiological, nuclear and explosives (CBRN-E) threats, CEA is studying the detection of Special Nuclear Materials (SNM) by neutron interrogation with fast neutrons produced by an associated particle sealed tube neutron generator. The deuterium-tritium fusion reaction produces an alpha particle and a 14 MeV neutron almost back to back, allowing tagging neutron emission both in time and direction with an alpha particle position-sensitive sensor embedded in the generator. Fission prompt neutrons and gamma rays induced by tagged neutrons which are tagged by an alpha particle are detected in coincidence with plastic scintillators. This paper presents numerical simulations performed with the MCNP-PoliMi Monte Carlo computer code and with post processing software developed with the ROOT data analysis package. False coincidences due to neutron and photon scattering between adjacent detectors (cross talk) are filtered out to increase the selectivity between nuclear and benign materials. Accidental coincidences, which are not correlated to an alpha particle, are also taken into account in the numerical model, as well as counting statistics, and the time-energy resolution of the data acquisition system. Such realistic calculations show that relevant quantities of SNM (few kg) can be distinguished from cargo and shielding materials in 10 min acquisitions. First laboratory tests of the system under development in CEA laboratories are also presented.