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一维水动力学降阶模型研究

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一维水动力学模型是非线性复杂系统,长时段模拟常常耗费大量计算资源和时间,给防洪预报预警工作带来挑战.为了提高计算效率,基于本征正交分解(POD)和离散经验插值方法(DEIM),通过投影和插值降低一维水动力学全阶模型的阶数,构建POD模型和POD-DEIM模型.将模型应用于矩形明渠的数值实验中,结果显示:与全阶模型相比,POD模型和POD-DEIM模型的前3个模态捕捉到99％以上的能量,近似的水深误差小于0.1m,单宽流量误差小于0.6m2/s,POD模型加速比为51倍,POD-DEIM模型加速比为111倍,表明降阶模型具有较高的精度和效率,适用于一维水动力学模型加速计算.
Research on 1D Hydrodynamic Reduced Order Model
The 1D hydrodynamic model is a nonlinear complex system.Long-term simulation often consumes a lot of computing resources and time,bringing challenges to flood control forecasting and early warning.To improve the computational efficiency,the POD model and POD-DEIM model were constructed based on the Proper Orthogonal Decomposition(POD)and the Discrete Empirical Interpolation Method(DEIM)to reduce the order of the 1D hydrodynamic full-order model through projection and interpolation.The model is applied to the numerical experiment of a rectangular open channel.The results show that the first three modes of the POD model and the POD-DEIM model capture more than 99％of the energy of the full-order model.The approximate water depth error is less than 0.1m and the flow per unit width error is less than 0.6m2/s.The speedups of the POD model and POD-DEIM model are 51 times and 111 times,respectively.The results indicate that the reduced order model has high accuracy and efficiency performance and is suitable for the accelerated computation of 1D hydrodynamic models.

Saint-Venant's equationsreduced order modelsproper orthogonal decomposition(POD)discrete empirical interpolation method(DEIM)modenonlinear systemaccelerated computationpartial differential equation

卢家波、尹志杰、向小华、吴晓玲

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河海大学水文水资源学院,江苏南京 210098

水利部信息中心(水利部水文水资源监测预报中心),北京 100053

圣维南方程组 降阶模型 本征正交分解(POD) 离散经验插值方法(DEIM) 模态 非线性系统 加速计算 偏微分方程

国家重点研发计划项目

2023YFC3006501

2024

10.16058/j.issn.1005-0930.2024.05.004

应用基础与工程科学学报
中国自然资源学会

应用基础与工程科学学报

CSTPCD北大核心
影响因子：0.895
ISSN：1005-0930
年,卷(期)：2024.32(5)