基于旋转x-t平面的河渠水流反向演算  

Reverse flow routing in rivers on the rotated x-t plane

作　　者：王家彪 赵建世 雷晓辉[2] 王浩[1,2] 廖卫红[2] WANG Jiabiao;ZHAO Jianshi;LEI Xiaohui;WANG Hao;LIAO Weihong(State Key Laboratory of Hydroscience and Engineering,Tsinghua University,Beijing 100084,China;China Institute of Water Resources and Hydropower Research,Beijing 100038,China)

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [2]中国水利水电科学研究院,北京100038

出　　处：《清华大学学报（自然科学版）》2020年第10期855-863,共9页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(91747208,51579129)。

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。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 

分 类 号：X522[环境科学与工程—环境工程]