4.2 Parallel performance analysis

To test the parallel performance of the model,two different mesh sizes were used to divide the study area.

Scheme 1: mesh size 30 m, giving 131 855 cells and 136 948 nodes.

Scheme 2: mesh size 20 m, giving 253 161 cells and 260 579 nodes.

Table 1 Water depth and flow velocity verificationFlow/ m3·s-1Hydrological station Water depth/m Flow velocity/m·s-1Measured CalculatedDeviationMeasuredCalculated Deviation Relative deviation Nian Pantuo 181.78 181.77 -0.01 0.85 0.83 -0.02 -2.4%QYangtze=3 850,QJialing=630 Ta Ping 180.31 180.26 -0.05 1.06 1.09 0.03 2.8%Shuang 176.22 0 1.15 1.17 0.02 1.7%Xiao Nanhai 174.69 174.61 -0.08 0.80 0.79 -0.01 -1.3%Diao Erzui 170.57 170.56 -0.01 1.17 1.19 0.02 1.7%Luo 167.22 0.02 1.79 1.83 0.04 2.2%E Gongyan 164.65 164.63 -0.02 1.53 1.52 -0.01 -1.0%Cun Tan 162.65 162.66 0.01 1.07 1.04 -0.03 -2.8%Tong 162.42 -0.08 1.22 1.27 0.05 4.1%Nian Pantuo 189.62 189.57 -0.05 1.41 1.47 0.06 4.3%QYangtze=,QJialing=1600 Ta Ping 187.42 187.39 -0.03 1.38 1.40 0.02 1.4%Shuang 183.46 -0.02 2.22 2.15 -0.07 -3.2%Xiao Nanhai 181.30 181.36 0.06 1.89 1.93 0.04 2.1%Diao Erzui 178.04 178.05 0.01 1.90 1.91 0.01 1.0%Luo 175.27 0.02 2.23 2.04 0.01 0.4%E Gongyan 172.77 172.74 -0.03 2.05 2.04 -0.01 -0.5%Cun Tan 169.53 169.51 -0.02 2.01 1.96 -0.05 -2.5%Tong 168.65 -0.08 1.85 1.88 0.03 1.6%Nian Pantuo 193.78 193.76 -0.02 1.64 1.68 0.04 2.4%QYangtze=Q ,Jialing=4130 Ta Ping 191.27 191.22 -0.05 1.80 1.77 -0.03 -1.7%Shuang 187.28 0.08 2.33 2.34 0.01 0.4%Xiao Nanhai 185.29 185.30 0.01 2.42 2.40 -0.02 -1.0%Diao Erzui 182.19 182.25 0.06 2.51 2.54 0.03 1.2%Luo 179.89 0.05 2.77 2.76 -0.01 -0.4%E Gongyan 177.82 177.77 -0.05 2.63 2.61 -0.02 -1.0%Cun Tan 173.86 173.83 -0.03 2.40 2.43 0.03 1.3%Tong 173.24 0.08 2.34 2.32 -0.02 -1.0%

Table 2 Time (s), speedup, efficiency (%) and time-saving ratio (%) of different calculation schemes on platform 1Grid number - Serial calculation Parallel calculation 2 4 8 12 16 20 Calculation time/s 2 151 1 115 590 305 209 161 132 131 855Speedup - 1.93 3.65 7.06 10.29 13.39 16.30 Efficiency - 97% 92% 88% 86% 84% 82%Saving time ratio - 52% 73% 86% 90% 93% 94%Calculation time/s 4 379 2 075 1 106 579 391 301 246 253 161Speedup - 2.11 3.96 7.56 11.20 14.56 17.80 Efficiency - 106% 99% 95% 93% 91% 89%Saving time ratio - 53% 75% 87% 91% 93% 94%

Table 3 Time (s), speedup, efficiency (%) and time-saving ratio (%) of different calculation schemes on platform 2Grid number - Serial calculation Parallel calculation 16 32 48 64 80 96 112 128 Calculation time/s 5 845 540 356 312 290 258 232 221 217 131 855Speedup - Efficiency - 68% 51% 39% 31% 28% 26% 24% 21%Saving time ratio - 91% 94% 95% 95% 96% 96% 96% 96%Calculation time/s 12 529 997 575 469 453 445 416 384 359 253 161Speedup - Efficiency - 79% 68% 56% 43% 35% 31% 29% 27%Saving time ratio - 92% 95% 96% 96% 96% 97% 97% 97%

The parallel model was executed on two different computing platforms to test its performance. The main configuration parameters of the different platforms are as follows:

Platform 1: two Intel E5-2680 V2 2.80 GHz processors, 20 physical cores, 64 GB memory, and the Intel Visual Fortran Composer XE 2013 SP1 compiler.

Platform 2: 32 Intel Xeon E5-4620 eight-core processors at 2.20 GHz, 256 physical cores, shared memory of 4 TB, NUMA architecture, and the Intel Visual Fortran Composer XE 2013 SP1 compiler.

In the process of parallel computing, Platform 1 calls 2, 4, 8, 12, 16, and 20 threads, whereas Platform 2 calls 16, 32, 48, 64, 80, 96, 112, and 128 analyzed the speedup, efficiency, and time-saving ratio of the models. The results are given in Tables 2,3.

The speedup ratio S is calculated as follows

where TSis the serial computation time and TPis the parallel computation time.

Efficiency E is calculated as follows

where n is the number of threads.

The time-saving ratio δT is calculated as follows

4.3 Navigable flow simulation speed

From Tables 2, 3, we can see that the shortest flow condition calculation time is 2.2 min (132 s) in scheme 1 and 4.1 min (246 s) in scheme 2. Using the flow scheme database to obtain the flow conditions,approximately 10 s is required for interpolation, which fully satisfies the real-time requirements of the , with the combination of the 2-D parallel model and the flow scheme database, the flow condition simulation system can supply detailed flow information for shipping when the changes in flow discharge are relatively slow. When extreme flow conditions occur in the upper reaches of the river system, such as during a flood or surge event, the speed of the model will enable an early warning to be supplied to ships downstream.

5. Discussion

5.1 Acceleration effect analysis

The simulation time of the proposed system is influenced by the computational load and the the number of grid cells increases, both the serial and parallel computing time increase, although the speedup and efficiency also increase.

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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