Numerical Simulations of 2D Hydraulic Jumps by a Parallel SPH Model

Hydraulic jumps are a rapid transition from supercritical to subcritical flow and generally occur in rivers or spillways. Owing to the high energy dissipation rate, hydraulic jumps are widely applied as energy dissipators in hydraulic projects. To achieve efficient and accurate simulations of 2D hydraulic jumps in open channels, a parallel Weakly Compressible Smoothed Particle Hydrodynamics model (WCSPH) with Shepard Density filter was established in this study. The acceleration of the model was obtained by OpenMP to reduce execution time. To further reduce execution time, a suitable and efficient scheduling strategy was selected for the parallel numerical model by comparing parallel speed-ups under different scheduling strategies in OpenMP. Following this, two test cases of uniform flow in open channels and hydraulic jumps with different inflow conditions were investigated to validate the model. The comparison of the water depth and velocity fields between the numerical results and the analytical solution generally showed good agreement, although there was a minor discrepancy in conjugate water depths. The numerical results showed free surface undulation with decreasing amplitude, which is more consistent with physical reality, with a low inflow Froude number. Simultaneously, the Shepard filter was able to smooth the pressure fields of the hydraulic jumps with a high inflow Froude number. Moreover, the parallel speed-up was generally able to reach theoretical maximum acceleration by analyzing the performance of the model according to different particle numbers.