基于旋转x-t平面的河渠水流反向演算

王家彪, 赵建世, 雷晓辉, 王浩, 廖卫红

清华大学学报（自然科学版） ›› 2020, Vol. 60 ›› Issue (10) : 855-863.

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清华大学学报（自然科学版） ›› 2020, Vol. 60 ›› Issue (10) : 855-863. DOI: 10.16511/j.cnki.qhdxxb.2020.22.015
水利水电工程

基于旋转x-t平面的河渠水流反向演算

  • 王家彪1, 赵建世1, 雷晓辉2, 王浩1,2, 廖卫红2
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Reverse flow routing in rivers on the rotated x-t plane

  • WANG Jiabiao1, ZHAO Jianshi1, LEI Xiaohui2, WANG Hao1,2, LIAO Weihong2
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摘要

水流反向演算在水利工程中应用广泛。由于水流具有沿程坦化的特性，直接反向求解水动力方程存在误差放大、结果不稳定的问题。该文将水流正向演算模型所在的x-t平面逆时针旋转90°后，构建了水流反向演算模型。该研究将正向模型的初始、边界条件分别变换为反向模型的边界、初始条件，解决了逆向数值迭代不稳定、不收敛的问题。经理想河道案例验证后，将反向模型应用于西江天然河道案例，结果表明模型稳定性好、模拟精度高，能有效反算出不同情景下的水流入流过程。该研究对于使用水流反向演算的水利工程具有实用价值。

Abstract

Reverse flow routing is widely used in hydraulic engineering calculations. However, numerical attenuation along the flow direction results in continuously amplified errors when directly solving the hydrodynamic equations in reverse which can lead to unstable calculations. This study contrarotates the x-t plane by 90° from the forward flow position and then derives the reverse flow routing model. On the rotated x-t plane, the initial and boundary conditions for the forward routing model are transformed to the boundary and initial conditions for the reverse model, which avoids the instabilities and non-convergence caused by reverse iterations in time and space. After validation, the reverse model is applied to a real-world case in the Xijiang River. The results show that this model is accurate and stable and can effectively reconstruct the historical inflow hydrographs for various flow cases. This research can improve hydraulic engineering studies using reverse flow routing.

关键词

反问题 / 稳定性 / 隐格式 / 水流演算

Key words

inverse problem / stability / implicit scheme / flow routing

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王家彪, 赵建世, 雷晓辉, 王浩, 廖卫红. 基于旋转x-t平面的河渠水流反向演算[J]. 清华大学学报（自然科学版）. 2020, 60(10): 855-863 https://doi.org/10.16511/j.cnki.qhdxxb.2020.22.015
WANG Jiabiao, ZHAO Jianshi, LEI Xiaohui, WANG Hao, LIAO Weihong. Reverse flow routing in rivers on the rotated x-t plane[J]. Journal of Tsinghua University(Science and Technology). 2020, 60(10): 855-863 https://doi.org/10.16511/j.cnki.qhdxxb.2020.22.015

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基金

赵建世,副教授,E-mail:zhaojianshi@tsinghua.edu.cn

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