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.

中文翻译：

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并行 SPH 模型对二维水力跳跃的数值模拟

水跃是从超临界流向亚临界流的快速转变，通常发生在河流或溢洪道中。由于能量耗散率高，水跃层在水利工程中被广泛用作消能器。为实现明渠二维水跃的高效、准确模拟，本研究建立了具有 Shepard 密度滤波器的并行弱可压缩平滑粒子流体动力学模型 (WCSPH)。模型的加速由 OpenMP 获得，以减少执行时间。为了进一步减少执行时间，通过比较OpenMP中不同调度策略下的并行加速比，为并行数值模型选择了合适且有效的调度策略。按照此，研究了明渠均匀流动和不同流入条件下水跃的两个测试案例，以验证模型。数值结果与解析解之间的水深和速度场的比较总体上显示出良好的一致性，尽管共轭水深存在微小差异。数值结果显示自由表面波动幅度减小，这更符合物理现实，流入弗劳德数较低。同时，Shepard 过滤器能够平滑具有高流入弗劳德数的水跃压力场。此外，通过根据不同粒子数分析模型的性能，并行加速一般能够达到理论最大加速度。