运动波方程的特征有限元数值模拟  

Numerical Simulation for the Kinematic Wave Equation Based on Characteristic Finite Element Method

作　　者：田东方[1] 李学斌[1] 王正中 

机构地区：[1]三峡大学水利与环境学院,湖北宜昌443002 [2]湖北三江航天江河化工科技有限公司,湖北宜昌444299

出　　处：《水力发电》2016年第7期103-106,共4页Water Power

基　　金：国家自然科学基金青年项目(41302275)

摘　　要：推导了运动波方程的特征有限元格式,实现了该方程的特征有限元数值模拟。借助正交试验法,以解析解为参考,分析了一定净雨强、坡长、坡角、Manning糙率条件下,有限元单元尺寸、计算时间步长以及允许误差等因素对数值解误差的影响。分析结果表明,在净雨强均匀分布的情况下,数值解与解析解的误差沿坡顶至坡脚快速减小;最大误差均出现在靠近坡顶边界的节点处;误差受单元尺寸影响最大,而时间步长和允许误差相对较小。A program for numerical simulation of the kinematic wave equalion corresponding to characteristic finite element method is coded. Compared with analytical solution, the influence of element scale, calculation time step and tolerance of the error of numerical simulation are studied under a certain net rainfall intensity, slope length, slope gradient and Manning roughness. The results indicate that, when rainfall is distributed uniformly, the error of water depth reduces quickly from the top of slope to the toe of slope and the error reaches its climax at the node which is near to top slope. Among three factors mentioned above, the element scale is most influential, while two others have little influence.

关 键 词：运动波方程 特征有限元 数值模拟 误差 

分 类 号：TU43[建筑科学—岩土工程]