深入认识大型江湖系统水动力特性,需要使用平面二维数学模型代替传统一维数学模型开展模拟和研究。当以高分辨率计算网格作为前提时,大型江湖系统二维水动力模型“计算精度与效率”的矛盾则转化为计算效率瓶颈。以荆江-洞庭湖系统为背景(剖分为32.8万个四边形单元,最小网格尺度约50 m),选用MIKE21模型和一种半隐式欧拉-拉格朗日模型,开展大型江湖系统显式、隐式水动力模型性能的比较研究,探讨大型江湖系统高分辨率二维模型的可实用性。研究结果表明:显式模型稳定性较差,允许的最大时间步长为0.8 s;隐式模型稳定性好,时间步长可达60 s以上;在常规16核工作站的效率测试结果表明,显式模型具有良好的可并行性,加速比随核心数量基本呈现线性变化;隐式模型(使用预测-校正分块并行计算方法)亦可取得非常大的加速比,在16核心并行条件下加速比Sp可达11.1;模拟荆江-洞庭湖系统1年的非恒定流过程,显式、隐式模型的耗时分别为411、10.76 h(16核),后者计算效率是前者的38.2倍,可满足大型江湖系统整体高分辨率平面二维水动力模拟的实用性要求。
Abstract
To deeply understand the hydrodynamic characteristics of large-scale river-lake system, two-dimensional(2D) mathematical model instead of traditional one-dimensional(1D) model is required for simulation and research when calculation accuracy is given higher priority than calculation efficiency. With high-resolution grid as the premise, the contradiction between accuracy and efficiency of 2D hydrodynamic model turns into a bottleneck of calculation efficiency. With the Jingjiang-Dongting (JDT) system (divided into 328 000 quadrilateral cells with the minimum grid scale about 50 m) as research background, the performances of both explicit and implicit hydrodynamic models for large-scale river-lake system were compared using MIKE21 model and a semi-implicit Eulerian-Lagrangian model. The practicability of high-resolution 2D models of large-scale river-lake systems was also discussed. Results illustrated that explicit model is less stable (maximum allowable time step 0.8 s) than implicit model (time step reaching over 60 s). The efficiency test results on a conventional 16-core workstation revealed sound parallelism of explicit model, with the speedup ratio varying linearly with the number of cores. Implicit model (using the prediction-correction block parallel computing method) can also achieve a very large speedup ratio, amounting to 11.1 under 16-core parallel conditions. The explicit and implicit models took 411 and 10.76 hours (16 cores), respectively, to simulate the one-year unsteady flow in JDT system. The calculation efficiency of the latter is 38.2 times higher than that of the former. In conclusion, implicit model meets the practical requirements of high-resolution 2D hydrodynamic simulation for large-scale river-lake system.
关键词
大型江湖系统 /
高分辨率水动力模型 /
显式模型 /
隐式模型 /
计算效率比较
Key words
large-scale river and lake system /
high-resolution hydrodynamic model /
explicit model /
implicit model /
comparison of calculation efficiency
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基金
国家自然科学基金项目(51779015);湖北省自然科学基金项目(2019CFB462)
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