In this work we investigated the possibility to predict the pressure drops across a patient-specific arterio-venous fistula (AVF) by means of an open-source hemodynamics solver aimed at convection-dominated incompressible flows. To account for the very high flow rates that develop in AVFs we considered a wide range of steady input flow conditions (corresponding to Reynolds numbers 100, 200, 550, 1000, 1500, and 2000), and compared with experiments for over 200 flow rates, up to Reynolds 2000. Three meshes for the numerical model, based on a micro-CT acquisition of the in vitro silicon model, were generated, in order to perform a h-refinement study and assess the mesh density allowing to correctly estimate the losses across the anastomosis. For the sake of validation, in addition to pressure assessment, the velocity solutions for Re 550 and 1000 were compared with particle image velocimetry (PIV) acquisitions. Once the solver was validated we also simulated pulsatile input flow conditions to investigate the role of pulsatility in predicting pressure drops. When the finer grid is considered almost all the experimental values for the pressure drop vs. flow measurements are within the standard deviation range of the numerical pressure drops. For the PIV validation, a good agreement is observed between in vitro data and numerical results. The ability to simulate unstable convection-dominated flows in complex 3D geometries is demonstrated and more insight is obtained about the non-common physiological flow conditions induced by fistula creation.