For example, when platform 2 calls 128 threads,the speedup with mesh scheme 1 is 26.93 and the speedup with mesh scheme 2 is 34.94. When platform 1 calls 20 threads, the efficiency with mesh scheme 1 is 82% and the efficiency with mesh scheme 2 is 89%.It can be seen that the parallel acceleration effect is more obvious with higher computational loads.

Fig. 6 (Color online) The navigable flow condition simulation visualization

The model has achieved the purpose of parallel acceleration on two different platforms, but the calculation time, speedup, efficiency, and time-saving ratio are different. From Tables 2, 3, we can see that:(1) The minimum computation times with mesh schemes 1 and 2 are 132 s and 246 s, respectively, on platform 1, and 217 s and 359 s, respectively, on platform 2. This indicates that the model performance is better on platform 1 than on platform 2. (2) The maximum speedup ratios of mesh schemes 1 and 2 are 16.30 and 17.80, respectively, on platform 1, and 26.93 and 34.94, respectively, on platform 2, which shows that the number of physical cores is the main factor affecting the speedup ratio. (3) On platform 1,the model is generally very efficient, and only a small reduction in efficiency is apparent as the number of threads increases, demonstrating that platform 1 has a higher degree of resource utilization than platform 2.The computing speed and data transmission efficiency of platform 1 are very high, and the computation time is low when the calculation task is small. However,the small number of physical cores on platform 1 makes it difficult to maintain a fast computing speed as the computing task becomes more 2 has many physical cores, so it has greater computing potential and can be used for large-scale computing tasks. However, the low computation speed and poor data transmission efficiency mean that additional time is needed as well as computational resources. Generally, besides the number of physical cores and dominant frequency, the connection and integration of the physical cores also affects the acceleration effect. Platforms with high levels of connection and integration will perform better than those with poor connection and integration in terms of parallel acceleration. Thus, platforms with fewer physical cores that are better connected and integrated(e.g., platform 1) are more suitable for parallel computing tasks with small computational loads. In contrast, platforms with more physical cores but a lower level of connection and integration (e.g.,platform 2) are better suited to larger computational loads.

5.2 System application

The navigable flow condition simulation system not only provides more detailed information about the water depth, but also provides the flow velocity distribution. When the flow condition changes suddenly, the system determines these flow changes through the simulation, providing sufficient reaction time for downstream ships to avoid accidents. The system can be combined with meteorological information to simulate the flood process. The parallel model will reduce the computation time, enabling the flood propagation process and corresponding propagation time to be determined in advance and providing a reference for the safety of downstream ships. For example, when the flow of the study area increases from 15 000 m3/s to 35 000 m3/s and the flood propagation time is about 4 h, the 2-D parallel model requires only 4 min to simulate the flow condition,providing plenty of time for downstream ships to react.

In addition, the system provides warning information to any ships with a targeted flow, achieving maximum use of waterway resources. For example,for a 1 000 t ship, the scope for navigation varies depending on whether the flow in a waterway is, e.g.,20 000 m3/s or 30 000 m3/s. Similarly, when the flow in a waterway is 30 000 m3/s , the scope for navigation will depend on whether the ship weighs,e.g., 1 000 t or 3 000 t. Traditional aids to navigation and electronic navigation charts cannot reflect changes in the scope of navigation for different ships in different flow conditions and areas that have very large flow velocities or a vortex. That is, they cannot divide the scope for navigation, leading to a waste of waterway resources. However, the navigable flow condition simulation system can obtain the distribution of water depth (h) and flow velocity (v) from the model (see Figs. 6(a), 6(b)), and according to the water depth and flow velocity threshold for each tonnage vessel, the system can show corresponding secure waterway. We can see from Figs. 6(c), 6(d)that different tonnage vessel has different secure scope,which is different with navigation mark system. In addition, for the same tonnage vessel, the secure scope is different in different river discharge (see Fig. 6(d)).With all these timely status information, the vessels can make full use of secure waterway resources that change according to river discharge.

6. Conclusions

The rapid simulation of navigable flow conditions can provide detailed and timely information for ship navigation, which is beneficial to improving the safety of navigation. In this paper, we have studied the flow simulation module of a navigable flow condition simulation system. A navigable flow simulation model based on 2-D hydrodynamic equations was established, and an explicit finite volume method was used to solve the model equations. To achieve parallel acceleration, OpenMP was adopted, as the calculations in each grid cell are not related in each time step,so they can be calculated separately on different computation cores. The following conclusions can be drawn.

文章来源：《水动力学研究与进展》 网址: http://www.sdlxyjyjzzz.cn/qikandaodu/2021/0114/463.html

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