Surface flow formula (Water Overlay) - Revision history

Rudolf@tygron.nl at 11:27, 25 February 2026

2026-02-25T11:27:22Z

← Older revision		Revision as of 11:27, 25 February 2026
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	\|page=		\|page=
	\|source=		\|source=
	\|link=~~http~~://~~www.math~~.tamu.edu/~gpetrova/KPSV.pdf		\|link=https://people.tamu.edu/~gpetrova//KPSV.pdf
	\|lastvisit=2019-04-11		\|lastvisit=2019-04-11
	}}		}}

Rudolf@tygron.nl at 13:34, 17 October 2025

2025-10-17T13:34:31Z

← Older revision		Revision as of 13:34, 17 October 2025
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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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	{{article end		{{article end
	\|seealso=		\|seealso=
	* [[Surface model (Water Overlay)~~\|Surface model~~]]		* [[Surface model (Water Overlay)]]
	* [[Result type (Water Overlay)~~\|Water overlay result types~~]]		* [[Result type (Water Overlay)]]
	* [[~~Manning_value_~~(~~Function_Value~~)~~\|Manning value~~]]		* [[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>
	}}		}}
	{{~~Template:~~WaterOverlay formula nav}}
			{{WaterOverlay formula nav}}

Frank@tygron.nl at 09:03, 29 January 2024

2024-01-29T09:03:40Z

← Older revision		Revision as of 09:03, 29 January 2024
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	\|}		\|}

	~~==See also=~~=		{{article end
			\|seealso=
	* [[Surface model (Water Overlay)\|Surface model]]		* [[Surface model (Water Overlay)\|Surface model]]
	* [[Result type (Water Overlay)\|Water overlay result types]]		* [[Result type (Water Overlay)\|Water overlay result types]]
	* [[Manning_value_(Function_Value)\|Manning value]]		* [[Manning_value_(Function_Value)\|Manning 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 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>		</references>
			}}
	{{Template:WaterOverlay formula nav}}		{{Template:WaterOverlay formula nav}}

Frank@tygron.nl at 13:36, 1 February 2021

2021-02-01T13:36:25Z

← Older revision		Revision as of 13:36, 1 February 2021
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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>

Rudolf@tygron.nl at 12:03, 14 August 2020

2020-08-14T12:03:59Z

← Older revision		Revision as of 12:03, 14 August 2020
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	</references>		</references>

	{{Template:~~WaterOverlay_nav~~}}		{{Template:WaterOverlay formula nav}}

Frank@tygron.nl: /* See also */

2020-07-10T15:06:49Z

See also

← Older revision		Revision as of 15:06, 10 July 2020
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	==See also==		==See also==
			* [[Surface model (Water Overlay)\|Surface model]]
	* [[Result type (Water Overlay)\|Water overlay result types]]		* [[Result type (Water Overlay)\|Water overlay result types]]
	* [[Manning_value_(Function_Value)\|Manning value]]		* [[Manning_value_(Function_Value)\|Manning value]]

Frank@tygron.nl: /* See also */

2020-07-10T15:01:16Z

See also

← Older revision		Revision as of 15:01, 10 July 2020
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	==See also==		==See also==
	* [[Result ~~types~~ (Water Overlay)]]		* [[Result type (Water Overlay)\|Water overlay result types]]
	* [[Manning_value_(Function_Value)\|Manning value]]		* [[Manning_value_(Function_Value)\|Manning value]]

Frank@tygron.nl: /* See also */

2020-07-10T15:00:51Z

See also

← Older revision		Revision as of 15:00, 10 July 2020
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	==See also==		==See also==
			* [[Result types (Water Overlay)]]
	* [[Manning_value_(Function_Value)\|Manning value]]		* [[Manning_value_(Function_Value)\|Manning value]]

Frank@tygron.nl: /* See also */

2020-07-10T14:59:56Z

See also

← Older revision		Revision as of 14:59, 10 July 2020
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	==See also==		==See also==
	* [[Manning_value_(Function_Value)]\|Manning value]]		* [[Manning_value_(Function_Value)\|Manning value]]

	==References==		==References==

Frank@tygron.nl: /* See also */

2020-07-10T14:59:47Z

See also

← Older revision		Revision as of 14:59, 10 July 2020
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	==See also==		==See also==
	* [[Manning_value_(Function_Value)]\|Manning value]		* [[Manning_value_(Function_Value)]\|Manning value]]

	==References==		==References==