Abstract
A new sweep-search algorithm (SSA) is developed and tested to identify the channel geometry transitions responsible for numerical convergence failure in a Saint-Venant equation (SVE) simulation of a large-scale open-channel network. Numerical instabilities are known to occur at “sharp” transitions in discrete geometry, but the identification of problem locations has been a matter of modeler’s art and a roadblock to implementing large-scale SVE simulations. The new method implements techniques from graph theory applied to a steady-state 1D shallow-water equation solver to recursively examine the numerical stability of each flowpath through the channel network. The SSA is validated with a short river reach and tested by the simulation of ten complete river systems of the Texas–Gulf Coast region by using the extreme hydrological conditions recorded during hurricane Harvey. The SSA successfully identified the problematic channel sections in all tested river systems. Subsequent modification of the problem sections allowed stable solution by an unsteady SVE numerical solver. The new SSA approach permits automated and consistent identification of problem channel geometry in large open-channel network data sets, which is necessary to effectively apply the fully dynamic Saint-Venant equations to large-scale river networks or for city-wide stormwater networks.
Highlights
Solution of the full unsteady Saint-Venant equations (SVE) across large-scale openchannel networks has been shown to be computationally practical [1], but there remain a variety of roadblocks to effective and efficient applications for regional-to-continental scale river systems or city-wide stormwater networks
Neither issue has been previously investigated in the literature. As this is the first study of numerical instabilities for large-scale flow networks simulated with implicit time-marching of the Saint-Venant equations, we focus solely on the issue of identifying troublesome geometry locations using an automated approach that is demonstrated at regional river network scales and is arguably practical at continental scales
The bottom slope of Waller Creek with the closely-surveyed cross-sections includes sharp slope discontinuities, which are replaced with uniform slopes so that we focus on effects of sharp-transition channel geometry and exclude instabilities caused by a discontinuous bottom slope as these were treated in Yu et al [3]
Summary
Solution of the full unsteady Saint-Venant equations (SVE) across large-scale openchannel networks has been shown to be computationally practical [1], but there remain a variety of roadblocks to effective and efficient applications for regional-to-continental scale river systems or city-wide stormwater networks. SVE models (e.g., unsteady HEC-RAS [2]) are well-aware of such problems, typically using past experience and “engineering judgement” to smooth or remove troublesome geometry and obtain stable simulations Such ad hoc fixes are readily applied in reach-scale hydraulic simulations where the location of the simulation instability and the appropriate fix can be diagnosed by simple visualization of results and trial-and-error geometry adjustments. The transition from hydrologic network models to hydraulic network models has often been accompanied by the use simplified cross-sectional shapes [7,10,11,12], which are typically derived from hydrological characteristics such as cumulative drainage area or mean annual flow that change gradually through space [12,13,14,15,16] Such approaches result in smooth geometry that is unlikely to cause instabilities and oscillations. Simple insertion of higher-resolution geometry into an existing, stable hydraulic model can lead to instabilities and oscillations due to sharp features in the high-resolution geometry
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