Surface flow formula (Water Overlay): Difference between revisions

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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):
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>
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\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>
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|}
|}


==See also==
{{article end
* [[Surface model (Water Overlay)|Surface model]]
|seealso=
* [[Result type (Water Overlay)|Water overlay result types]]
* [[Surface model (Water Overlay)]]
* [[Manning_value_(Function_Value)|Manning value]]
* [[Result type (Water Overlay)]]
 
* [[Manning value (Function Value)]]
==References==
|references=
<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>
{{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>
</references>
}}


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{{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)
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