A semidiscrete finite volume formulation for multiprocess watershed simulation
A semidiscrete finite volume formulation for multiprocess watershed simulation
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DOI：
10.1029/2006wr005752
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发表时间：
2007-08
影响因子：
5.4
通讯作者：
Yizhong Qu;C. Duffy
中科院分区：
文献类型：
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作者：
Yizhong Qu;C. Duffy
陆地水循环中的水文过程在广泛的时间和空间尺度上运行，并且其控制方程可以是常微分方程（ODE）和偏微分方程（PDE）的混合。在本文中，我们提出了一个统一的战略，制定和解决方案的完全耦合的过程方程在流域和流域尺度。该策略显示了如何使用半离散有限体积法（FVM）的混合方程系统可以局部减少到常微分方程。区域分解将流域表面划分到非结构化网格上，每个单元的垂直投影形成一个有限体积，所有物理过程方程都形成在该有限体积上。投影的体积或棱柱被划分为表面层和次表面层，导致完全耦合的局部ODE系统，称为模型“内核”。全局ODE系统通过组合域上的局部ODE系统来组装，然后由最先进的ODE求解器求解。基于Delaunay三角剖分的非结构化网格，与相关的河流网络，流域边界，高程等高线，植被，地质等的约束，然后投影到不规则的网络的基础几何和参数字段。基于核的公式简化了添加或删除状态、本构律或闭合关系的过程。该策略在宾夕法尼亚州中部的页岩山实验流域进行了演示，并观察到几个现象：（1）奴役原则被证明是高地流域浅层土壤水分-地下水位动态的有用近似;（2）耦合显示了前期水分（即，初始条件）可以放大峰值流量;（3）耦合方程预测了高地短暂河道流量的开始或阈值;（4）模型显示了微地形信息如何控制页岩山场地的地表饱和度和地表水流路径的连通性。在这项研究中开发的开源代码被称为宾州综合水文模型（PIHM）。
Hydrological processes within the terrestrial water cycle operate over a wide range of time and space scales, and with governing equations that may be a mixture of ordinary differential equations (ODEs) and partial differential equations (PDEs). In this paper we propose a unified strategy for the formulation and solution of fully coupled process equations at the watershed and river basin scale. The strategy shows how a system of mixed equations can be locally reduced to ordinary differential equations using the semidiscrete finite volume method (FVM). Domain decomposition partitions the watershed surface onto an unstructured grid, and vertical projection of each element forms a finite volume on which all physical process equations are formed. The projected volume or prism is partitioned into surface and subsurface layers, leading to a fully coupled, local ODE system, referred to as the model “kernel.” The global ODE system is assembled by combining the local ODE system over the domain, and is then solved by a state‐of‐the‐art ODE solver. The unstructured grid, based on Delaunay triangulation, is generated with constraints related to the river network, watershed boundary, elevation contours, vegetation, geology, etc. The underlying geometry and parameter fields are then projected onto the irregular network. The kernel‐based formulation simplifies the process of adding or eliminating states, constitutive laws, or closure relations. The strategy is demonstrated for the Shale Hills experimental watershed in central Pennsylvania, and several phenomena are observed: (1) The enslaving principle is shown to be a useful approximation for soil moisture–water table dynamics for shallow soils in upland watersheds; (2) the coupling shows how antecedent moisture (i.e., initial conditions) can amplify peak flows; (3) the coupled equations predict the onset or threshold for upland ephemeral channel flow; and (4) the model shows how microtopographic information controls surface saturation and connectivity of overland flow paths for the Shale Hills site. The open‐source code developed in this research is referred to as the Penn State Integrated Hydrologic Model (PIHM).