This work is devoted to the numerical simulation of liquid-vapour flows in nuclear framework. We investigate a simplified model, named Lmnc (for Low Mach Nuclear Core), describing the evolution of the coolant within a core of a Pressurized Water Reactor. This model, proposed in previous works, corresponds to the zero Mach asymptotic where the dilation of the fluid depends simply on the density of the fluid, function of the enthalpy. The goal of this work is to introduce a numerical approximation, validated on a reference test problem solved analytically, able to solve the 3D configuration.