基于有限差分法的扩散波沿程洪峰衰减值确定方法研究

• 作 者: 马海波 董晓华 王伟
• 机 构: 三峡大学水利与环境学院,水资源安全保障湖北省协同创新中心,南水北调中线干线工程建设管理局河南直管建管局,
• 出 处: 水电能源科学
• 发表日期: 2014年09期
• 关键词: 洪水波 洪水演算 洪峰流量 衰减值 有限差分法 中值定理 圣维南方程组 函数 变量 二阶导数

为了使洪水波在河道中的传播规律有更明确的物理意义,将洪峰流量表示为河道位置和传播时间的复合函数,通过拉格朗日中值定理和有限差分法推导该变量对河道位置的二阶导数与对传播时间的二阶导数之间的关系,进而推导出洪峰流量沿程衰减值的有限差分表达式,并通过实例对该公式进行了验证。结果表明,该洪峰流量衰减值公式中的洪峰流量值具有明确的传播位置及传播时间信息,能够刻画出洪峰流量的时空衰减规律,且计算结果精度较高。

In order to have a more explicit physical meaning of the flood wave propagation in the river, the peak flow is expressed as a composite function of the river position and propagation time. Lagrange’s median value theorem and finite difference method are used to deduce the influence of the variable on the river channel position The second derivative and the second derivative of the propagation time, and then deduces the finite difference expression of attenuation value along the peak flow. The formula is verified by an example. The results show that the peak flow value in the peak flow attenuation value formula has clear propagation position and propagation time information, which can characterize the spatial and temporal attenuation law of peak flow and the calculation accuracy is high.