In the last decades, 3D Concrete Printing (3DCP) has emerged as a rapidly evolving technology with promising applications in building design and construction, paving the way for innovative and sustainable building practices. This technology would bring numerous advantages, such as the possibility to easily build free-form topologically optimized shapes without the need for formwork and the reduction of human labour, construction times, and costs. However, prior to the large-scale adoption of 3DCP, it is still necessary to address numerous issues, both at the practical and numerical levels. In the specific, the development of reliable computational tools would provide a better understanding of the printing process, while also enabling to predict, in a design framework, its outcomes, in terms of material, structural and process performances. In our contribution we propose an innovative numerical model for the simulation of the printing process of cementitious materials, using a single-phase fluid approach. The motion of the fluid is governed by the Navier-Stokes equations with a non-Newtonian rheological law. To cope with the nonlinearities associated with the large deformations of the domain, the Particle Finite Element Method (PFEM) is used. Different numerical challenges, such as the imposition of the time-dependent moving boundary condition at the nozzle outlet and the accurate treatment of inter-layer contact, have been addressed and solved in the PFEM framework. Moreover, particular attention is given to the strategies for decreasing the computational cost, such as the use of an adaptive de-refinement technique. The model was validated against the experimental data in the literature for different printing scenarios and provided valuable insights into the printing process. It can be exploited to assess the extrudability of cementitious mixes given the rheological parameters, making it suitable to: support the experimental campaigns during the development of new cementitious inks; perform the optimization of the printing parameters; foresee the development of plastic and buckling failure during the printing of arbitrarily shaped objects.