Although the hydraulic transients in pipe systems are usually simulated by using a one-dimensional (1-D) approach, local three-dimensional (3-D) simulations are necessary because of obvious 3-D flow features in some local regions of the hydropower systems. This paper combines the 1-D method with a 3-D fluid flow model to simulate the Multi-Dimensional (MD) hydraulic transients in hydropower systems and proposes two methods for modeling the compressible water with the correct wave speed, and two strategies for efficiently coupling the 1-D and 3-D computational domains. The methods are validated by simulating the water hammer waves and the oscillations of the water level in a surge tank, and comparing the results with the 1-D solution data. An MD study is conducted for the transient flows in a realistic water conveying system that consists of a draft tube, a tailrace surge tank and a tailrace tunnel. It is shown that the 1-D-3-D coupling approach is an efficient and promising way to simulate the hydraulic transients in the hydropower systems in which the interactions between 1-D hydraulic fluctuations of the pipeline systems and the local 3-D flow patterns should be considered. Although the hydraulic transients in pipe systems are usually typically used by a one-dimensional (1-D) approach, local three-dimensional (3-D) simulations are necessary because of obvious 3-D flow features in some local regions of the hydropower systems. This paper combines the 1-D method with a 3-D fluid flow model to simulate the Multi-Dimensional (MD) hydraulic transients in hydropower systems and proposes two compressible water with the correct wave speed, and two strategies for efficiently coupling the 1-D and 3-D computational domains. The methods are validated by simulating the water hammer waves and the oscillations of the water level in a surge tank, and comparing the results with the 1-D solution data. An MD study is conducted for the transient flows in a realistic water conveying system that consists of a draft tube, a tailrace surge tank and a tailrace tunnel. It is shown that the 1-D-3-D coupling approach is an efficient and promising way to simu late the hydraulic transients in the hydropower systems in which the interactions between 1-D hydraulic fluctuations of the piping systems and the local 3-D flow patterns should be considered.