DOI: 10.5194/hess-23-1281-2019
论文题名: Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage
作者: Hodges B.R.
刊名: Hydrology and Earth System Sciences
ISSN: 1027-5606
出版年: 2019
卷: 23, 期: 3 起始页码: 1281
结束页码: 1304
语种: 英语
Scopus关键词: Finite volume method
; Hydrostatic pressure
; Topography
; Analytical approximation
; Finite volume element
; Irregular topography
; Large scale simulations
; Momentum conservation equations
; Saint Venant equation
; Urban drainage systems
; Water surface elevations
; Open channel flow
; finite difference method
; finite volume method
; hydrology
; hydrostatic pressure
; open channel flow
; river system
; urban drainage
英文摘要: New integral, finite-volume forms of the Saint-Venant equations for one-dimensional (1-D) open-channel flow are derived. The new equations are in the flux-gradient conservation form and transfer portions of both the hydrostatic pressure force and the gravitational force from the source term to the conservative flux term. This approach prevents irregular channel topography from creating an inherently non-smooth source term for momentum. The derivation introduces an analytical approximation of the free surface across a finite-volume element (e.g., linear, parabolic) with a weighting function for quadrature with bottom topography. This new free-surface/topography approach provides a single term that approximates the integrated piezometric pressure over a control volume that can be split between the source and the conservative flux terms without introducing new variables within the discretization. The resulting conservative finite-volume equations are written entirely in terms of flow rates, cross-sectional areas, and water surface elevations - without using the bottom slope (S0). The new Saint-Venant equation form is (1) inherently conservative, as compared to non-conservative finite-difference forms, and (2) inherently well-balanced for irregular topography, as compared to conservative finite-volume forms using the Cunge-Liggett approach that rely on two integrations of topography. It is likely that this new equation form will be more tractable for large-scale simulations of river networks and urban drainage systems with highly variable topography as it ensures the inhomogeneous source term of the momentum conservation equation is Lipschitz smooth as long as the solution variables are smooth. © Author(s) 2019. Citation statistics:
资源类型: 期刊论文
标识符: http://119.78.100.158/handle/2HF3EXSE/163029
Appears in Collections: 气候变化与战略
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作者单位: Hodges, B.R., National Center for Infrastructure Modeling and Management, University of Texas at Austin, Austin, TX, United States
Recommended Citation:
Hodges B.R.. Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage[J]. Hydrology and Earth System Sciences,2019-01-01,23(3)