Surface flow formula (Water Overlay): Difference between revisions

From Tygron Preview Support Wiki
Jump to navigation Jump to search
(Created page with "In the model, imbalances in the water surface elevation across the grid drive the flow of water until a state of equilibrium is reached in terms of ''w'' and flux. Behavior of...")
 
No edit summary
 
(13 intermediate revisions by 3 users not shown)
Line 1: Line 1:
In the model, imbalances in the water surface elevation across the grid drive the flow of water until a state of equilibrium is reached in terms of ''w'' and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)<ref name="Kurganov2"/>, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):
Imbalances in water levels across the grid drive the flow of water until a state of equilibrium is reached in terms of ''h'' (the height of the water column) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)<ref name="Kurganov2"/>, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):


:<math>
:<math>
Line 5: Line 5:
\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]
\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]
\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt]
\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt]
\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},
\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2v \sqrt{u^2 + v^2} h^{-\frac{4}{3}},
\end{align}
\end{align}
</math>
</math>
Line 24: Line 24:
| ''n'' || is the Gauckler–Manning coefficient
| ''n'' || is the Gauckler–Manning coefficient
|}
|}
{{article end
|seealso=
* [[Surface model (Water Overlay)|Surface model]]
* [[Result type (Water Overlay)|Water overlay result types]]
* [[Manning_value_(Function_Value)|Manning value]]
|references=
<references>
<ref name="Kurganov2">Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)</ref>
</references>
}}
{{Template:WaterOverlay formula nav}}

Latest revision as of 09:03, 29 January 2024

Imbalances in water levels across the grid drive the flow of water until a state of equilibrium is reached in terms of h (the height of the water column) and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)[1], which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):

where

u is the velocity in the x-direction
v is the velocity in the y-direction
h is the water depth
B is the bottom elevation
g is the acceleration due to gravity
n is the Gauckler–Manning coefficient

See also

References

  1. ↑ Kurganov A, Petrova G (2007) ∙ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf (last visited 2019-04-11)
Water Module
Benchmarks button.png
Introduction button.png
Water Module
Benchmarks button.png
Getting started button.png
Tutorials
Benchmarks button.png
Overview button.png
Overview
Benchmarks button.png
Theory button.png
Theory
Benchmarks button.png
Benchmarks button.png
Benchmarks
Models
Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas
Timestep • Season • Surface water level • Groundwater level
Flow formulas
Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas
Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related
Building attributes • Hydrological features • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data
Retrieved from "https://previewsupport.tygron.com/w/index.php?title=Surface_flow_formula_(Water_Overlay)&oldid=57910"