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
 
(14 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|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)]]
* [[Result type (Water Overlay)]]
* [[Manning value (Function Value)]]
|references=
<references>
{{ref|Kurganov2
  |name=A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
  |author=Kurganov A, Petrova G (2007)
  |page=
  |source=
  |link=http://www.math.tamu.edu/~gpetrova/KPSV.pdf
  |lastvisit=2019-04-11
}}
</references>
}}
{{WaterOverlay formula nav}}

Latest revision as of 13:34, 17 October 2025

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):

∂h∂t+∂(hu)∂x+∂(hv)∂y=0,∂(hu)∂t+∂∂x(hu2+12gh2)+∂(huv)∂y=−gh∂B∂x−ghn2uu2+v2h−43,∂(hv)∂t+∂(huv)∂x+∂∂y(hv2+12gh2)=−gh∂B∂y−ghn2vu2+v2h−43,

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. ↑ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ∙ Kurganov A, Petrova G (2007) ∙ Found at: http://www.math.tamu.edu/~gpetrova/KPSV.pdf ∙ (last visited: 2019-04-11)
Water Module
Water Module
Tutorials
Overview
Theory
Benchmarks
Models
Surface • Ground • Rain • Evapotranspiration • 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=63530"