冲积河流分级恒定水沙数学模型的适用性研究

Applicability of a quasi-steady flow model for alluvial rivers

天然河流的来流过程往往是非恒定的,特别是在洪水季节.在工程实践中为了简化计算,通常将非恒定来流过程概化为梯级形式的恒定流求解,相应的模型被称为分级恒定流模型.然而,分级恒定流模型与非恒定流模型之间的差异并不十分清楚.通过概化的长江中游长河段的数值算例来研究比较两种模型之间的差异,采用有限体积法中的SLC数值格式来求解非恒定流模型中的控制方程组,对于分级恒定流模型中的常微分方程组则采用有限差分法求解.研究结果表明,随着计算历时的增加,两种模型计算结果之间的差异逐渐变大.在模拟50年的冲淤变化时,分级恒定流模型与非恒定流模型计算总河段的冲淤量的相对差异为2.1%.随着河段距离的增加,两种模型计算河段的冲淤量相差越来越大.一般来说,分级恒定流模型可适用于短历时、短河段的情形;对于长历时、长河段水沙运动过程的模拟,推荐使用非恒定流模型.

Fluvial flows in natural rivers are typically characterized by unsteady hydrographs,especially in flood seasons.To improve the computation efficiency,however,an unsteady inflow hydrograph is usually approximated by several stepped steady hydrographs;and a simplified model for quasi-steady flows would be applied to engineering practice.Unfortunately,it remains poorly understanding about the performance of a quasi-steady flow model as compared to an unsteady flow model.So in this paper,a comparative study of the two models is presented by virtue of numerical cases of a generalized long channel in the middle reach of the Yangtze River.The governing equations in the unsteady flow model are numerically solved using Slope Limiter Centered（SLC）scheme in the framework of finite volume method,while the finite difference method is adopted to solve the ordinary differential equations in the quasi-steady flow model.It is shown that the differences between the results of the two models tend to be significant over time.Typically,the relative difference of the scouring and siltation volumes in the whole channel within 50 years between the two models is 2.1 percent.And the difference is greater as the river reach extends.Generally,the quasi-steady flow model could be appropriate for short-duration and short-reach cases,whilst unsteady flow model is applicable for long-duration and long-reach cases.