2019
DOI: 10.2478/johh-2019-0012
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Mathematical modeling of shallow-water flows on steep slopes

Abstract: A 2D hydrodynamic (labeled as CAR) model has been proposed in a rectangular Cartesian coordinate system with two axes within the horizontal plane and one axis along the vertical direction (global coordinates), considering the effects of bed slope on both pressure distribution and bed shear stresses. The CAR model satisfactorily reproduces the analytical solutions of dam-break flow over a steep slope, while the traditional Saint-Venant Equations (labeled as SVE) significantly overestimate the flow velocity. For… Show more

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Cited by 11 publications
(4 citation statements)
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“…Therefore, the FEI value obtained using S‐06 and S‐07 suggests a numerical error due to a combination of high flow velocity and large grid size. This may be related to assumptions in the Shallow Water Equations that do not hold for steep slopes (Denlinger & O'Connell, 2008; Ni et al, 2019). Interestingly, 29‐IN is no longer prioritised in the top 5 by simulation S‐08 (30 m grid size), implying that this grid size smooths out the slope sufficiently enough to reduce this error.…”
Section: Discussionmentioning
confidence: 99%
“…Therefore, the FEI value obtained using S‐06 and S‐07 suggests a numerical error due to a combination of high flow velocity and large grid size. This may be related to assumptions in the Shallow Water Equations that do not hold for steep slopes (Denlinger & O'Connell, 2008; Ni et al, 2019). Interestingly, 29‐IN is no longer prioritised in the top 5 by simulation S‐08 (30 m grid size), implying that this grid size smooths out the slope sufficiently enough to reduce this error.…”
Section: Discussionmentioning
confidence: 99%
“…This is especially relevant if sediment transport processes and granular flows are investigated. The differences between the use of a global coordinate system and a local coordinate system can be compensated by increasing the roughness parameter in a realistic range [91]. Additionally, the effects are relevant for events with long durations.…”
Section: Model Calibration and Validationmentioning
confidence: 99%
“…In particular, the optimization of the surface roughness in steep locations is impactful. This conclusion must be re-evaluated if a model is used with the formulation of the mathematical equations in a local coordinate system because this represents the flow characteristics more realistic at a steep surface [90,91]. In contrast, an optimization of the model parameters for an evaluation concerning the water depth does not have a large impact (UC = 12.41).…”
Section: High-impact Uncertainty Sourcesmentioning
confidence: 99%
“…Studies have documented that runoff processes in steep slopes or catchments are quite different from those with moderate slope [80,81]. Considering catastrophic flash floods often occur in steep catchments, it is therefore necessary to study the parameters estimation approach in order to better predict the occurrence of flash floods using hydrological models.…”
Section: Limitations and Future Directionsmentioning
confidence: 99%