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DOI	10.5194/hess-24-4001-2020
	A new form of the Saint-Venant equations for variable topography
	Yu C.-W.; Hodges B.R.; Liu F.
发表日期	2020
ISSN	1027-5606
起始页码	4001
结束页码	4024
卷号	24 期号:8
英文摘要	The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms. © Author(s) 2020.
语种	英语
scopus关键词	Rivers; Software testing; Topography; Algebraic transformations; Lipschitz continuous; Mathematical concepts; Model implementation; Numerical oscillation; Saint Venant equation; Smoothing algorithms; Smoothness conditions; Numerical methods; algorithm; equation; geometry; hydrological modeling; mathematical concept; numerical method; pressure gradient; slope; smoothing; tomography
来源期刊	Hydrology and Earth System Sciences
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/159328
作者单位	Yu, C.-W., National Center for Infrastructure Modeling and Management, University of Texas at Austin, Austin, Texas, United States; Hodges, B.R., National Center for Infrastructure Modeling and Management, University of Texas at Austin, Austin, Texas, United States; Liu, F., Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States,
推荐引用方式 GB/T 7714	Yu C.-W.,Hodges B.R.,Liu F.. A new form of the Saint-Venant equations for variable topography[J],2020,24(8).
APA	Yu C.-W.,Hodges B.R.,&Liu F..(2020).A new form of the Saint-Venant equations for variable topography.Hydrology and Earth System Sciences,24(8).
MLA	Yu C.-W.,et al."A new form of the Saint-Venant equations for variable topography".Hydrology and Earth System Sciences 24.8(2020).