In order to identify the leak source in complex heating pipeline networks, a timely and effective simulation of the leakage process was conducted. The open-source computational fluid dynamics software OpenFOAM 5.0 was combined with the PISO algorithm to simulate the pressure during the leakage in water supply networks, transforming the reverse source tracing problem into the solution of an adjoint equation. The validation of the transient adjoint equation for single-phase flow was completed through simulation, and the pressure wave change graph at the moment of the network leakage was solved, which was consistent with the experimental results. Using the open-source finite element analysis software OpenFOAM 5.0, the positioning accuracy of pipeline leak points can be controlled within the range from 92% to 96%. Based on the pressure wave change graph, the position of the leak source in the complex network was determined using the reverse source tracing method combined with the second correlation theory. The results show that the calculation speed of the PISO algorithm combined with the adjoint equation is significantly better than that of the individual SIMPLE and PISO algorithms, thereby proving the superiority of the adjoint method.