Abstract
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.
Highlights
A special hydraulic phenomenon, where the water depth in a short channel jumps sharply from less than the critical depth to greater than the critical depth, will occur when flow in an open channel transitions from subcritical to supercritical
The Weakly Compressible Smoothed Particle Hydrodynamics model (WCSPH) model was accelerated by the OpenMP
To further reduce execution time, the performance of the OpenMP-based Smoothed Particle Hydrodynamics method (SPH) code with different scheduling strategy was compared for the test case of hydraulic jumps
Summary
A special hydraulic phenomenon, where the water depth in a short channel jumps sharply from less than the critical depth to greater than the critical depth, will occur when flow in an open channel transitions from subcritical to supercritical. Level Set (LS) or Volume-of-Fluid (VOF) methods were necessary to capture the water surface in the Eulerian grid-based methods, due to the complexity of hydraulic jumps, such as large deformation and rapid change of flow filed. Other specific treatments, such as refining the mesh near the bed or jump zone, and reducing the time step, were needed to reproduce the characteristics of hydraulic jumps These specific treatments make it difficult and inefficient to solve the Euler model. The accuracy of the SPH model in computing hydraulic jumps was verified based on comparisons of water elevation, jump-toe position, jump depth, and the pressure on the basin bottom under different viscosity treatments. Though the SPH model has great advantages and has been adopted in some hydraulic jump numerical studies, it is inefficient due to the calculation of neighboring particle search, numerical viscosity, and particles interaction. The time step is calculated by a variable time step algorithm and updated in each step
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