This paper presents a sensitivity study of various CFD simulation parameters conducted in the case of a 2D axisymmetric ejector operating without induced flow. The influence of numerical parameters (solver, discretisation scheme, mesh and turbulence model) is investigated by comparing the various CFD results obtained (pressure, velocity, Mach number, and mass flow rate) with each other. The influence of the turbulence model is closely examined by comparing CFD results with the velocity measurements obtained by particle image velocimetry. The rules to be respected to achieve correct CFD simulation of the flow in supersonic ejectors are proposed. The use of the pressure-based coupled solver associated with the SST k-omega turbulence model is recommended. The terms of energy and pressure can be solved using first-order discretisation while the other equations (momentum, turbulent quantities) require second-order discretisation to correctly predict the supersonic flow with shocks.