Smoothed particle hydrodynamic simulation of an abruptly expanding transitional hydraulic jump

Hydraulic jumps in abruptly expanding horizontal channels involve intense energy dissipation and turbulent mixing, necessitating accurate simulation for the energy dissipator design. In order to address the limitations of mesh-based methods in capturing large free-surface deformations, this study develops a three-dimensional weakly compressible smoothed particle hydrodynamics (SPH) model using DualSPHysics. The model simulates the transitional jump (T-jump) evolution under different expansion ratios (B = 1.0–7.0) and inflow Froude numbers (Fr1 = 4.39–7.86), incorporating δ-SPH for the pressure stabilization, Sub-particle scale turbulence modeling, and the modified dynamic boundary condition. Experimental validation confirms the reliable prediction of surface profiles and velocity distributions. Results identify expansion ratio as the critical parameter: small ratios (B = 1.5–2.0) generate oscillating symmetric jumps, while larger ratios (B = 3.0–7.0) produce stable asymmetric jumps with large vortex structures. Energy dissipation increases with both the Froude number and expansion ratio, but reaches a plateau when B > 3.0, defining an optimal range of B = 3.0–4.0. It was also found that energy dissipation efficiency improves when the jump forms closer to the expansion outlet. This work demonstrates the advantages of the SPH method in modeling complex three-dimensional hydraulic jumps and provides support for the optimized stilling basin design.