This study introduces numerical advancements in an alternative design for the Super Proton Synchrotron (SPS) Beam Dump Facility (BDF) at the European Laboratory for Particle Physics (CERN). The design envisions a high-power operation target made of flowing liquid lead. The proposed BDF is a versatile facility for both beam-dump-like and fixed-target experiments. The target behavior is studied, assuming a proton beam with a momentum of 400 GeV/c, a pulse frequency of 1/7.2 Hz, and an average beam power of 355 kW. Using various Computational Fluid Dynamics (CFD) codes, we evaluate the behavior of liquid lead and predict the thermal stress on the target vessel induced by the pulsed heat source generated by the charged particle beam. The comparison increases the reliability of the results, investigating the dependencies on the CFD modeling approach. The beam is a volumetric heat source with data from the beam-lead interaction simulations provided by the European Laboratory for Particle Physics and obtained with a Monte Carlo code. Velocity field and stress profiles can enhance the design of the lead loop and verify its viability and safety when operated with a liquid metal target.