We present a numerical model for lahars generated by the mobilization of tephra deposits from a reference size eruption at Somma–Vesuvius. The paper presents the model (pyhsics and numerics) and a sensitivity analysis of the processes modelled, numerical schemes, and grid resolution. This work provides the basis for application to hazard quantification for lahars in the Vesuvius area. To this end, we rely on results of the two companion papers (Part 1 on field data, Part 3 on hazard maps).