非恒定水流计算的最优控制问题及其变分求解  

Optimal control problems in unsteady flow computation and their variational solutions

作　　者：赖锡军[1] 傅国圣 孙波[3] 

机构地区：[1]中国科学院南京地理与湖泊研究所湖泊与环境国家重点实验室,江苏南京210008 [2]扬泰水文水资源勘测局,江苏扬州225000 [3]山东省安丘市水利局,山东潍坊262100

出　　处：《水科学进展》2008年第4期537-545,共9页Advances in Water Science

基　　金：国家自然科学基金资助项目(5070903440571028)~~

摘　　要：为综合利用各类可用的信息源(如水流运动规律,观测资料和统计信息),在反问题的框架下构建了非恒定水流计算的变分模型。针对模型预测的可能误差来源,给出了初始条件、边界条件、物理参数三类独立参量及综合控制问题的定义。在此基础上,阐述了变分法求解这类偏微分方程最优化控制问题的基本原理及模型求解步骤。同时,为便于应用参考,选取初始条件、边界条件和物理参数作为控制向量,以实际常用的水流运动微分方程为基础,导出了一、二维非恒定水流计算的通用伴随方程。并以珠江黄浦至大虎段二维潮流计算为例,展示了变分模型的应用。Dynamical equations, observations and their statistics are all important information for presenting the states of unsteady flows. Under the framework of inverse problems, a variational model is developed to fuse all available information for improving the computation of unsteady flows. In the paper, the appropriate optimal control problems are firstly defined for controlling possible numerical errors from inaccurate initial conditions, boundary conditions and unknown physical parameters. Then, the general variational method and its numerical algorithm are suggested to solve these optimal control problems of unsteady flows. Also, purpose. It directly we derive the adjoint equations of one-and two-dimensional shallow equations serves for real engineering applications. With the of the Pearl River are investigated. Results show that the model can w proposed vail ell reconstruct ational model, with the forms for practical the tidal flows in one reach tidal flow states when data are unavailable at some boundaries, unlike the direct model.

关 键 词：非恒定流 反问题 变分法 最优控制 数据同化 数学模型 

分 类 号：TV133.2[水利工程—水力学及河流动力学]