MohidWiki - Recent changes [en]

Grids

2012-05-17T10:48:32Z

← Older revision		Revision as of 10:48, 17 May 2012
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−	#redirect [[Grid]]	+	!#redirect [[Grid]]
		+
		+	Mohid uses a Arakawa type C grid as described [http://journals.ametsoc.org/doi/abs/10.1175/1520-0493%281988%29116%3C2069%3AASISLF%3E2.0.CO%3B2 here]
		+
		+	Below are represented the different grids in the model, increasing in complexity, from property grids, adding velocity u grids and finally adding also velocity v grids.
		+
		+	Model properties grid has z's (or any property) in center and conceptually are similar to model volumes or cells.
		+	[[Image:PropertyGrid.png\|1000px\|thumb\|center\|]]
		+
		+
		+	Model velocity u's are at z's grid faces, in x direction. However, in velocity u grid, velocity u's are in center. z's (or properties) lie down in grid faces
		+	[[Image:VelocityUGrid.png\|1000px\|thumb\|center\|]]
		+
		+
		+	Model velocity v's are at z's grid faces, in y direction. However, in velocity v grid, velocity v's are in center. z's (or properties) lie down in grid faces and velocities u in corners. Also can be seen that velocity u's grid has velocity v's in its corners.
		+	[[Image:VelocityVGrid.png\|1000px\|thumb\|center\|]]

File:VelocityVGrid.png

2012-05-16T17:27:11Z

uploaded "[[File:VelocityVGrid.png]]"

Equations

2012-05-16T15:58:57Z

Moment Equation or "How those Properties Move":

← Older revision		Revision as of 15:58, 16 May 2012
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	The Newton's 2nd law and using density:		The Newton's 2nd law and using density:
−	[[Image:EqnQntMov Newton ~~FixedVol~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov Newton Masses.png\|1000px\|thumb\|center\|]]
−	where: x_i = spatial direction	+	where: x_i = spatial direction where velocity is solved
		+	x_j = all the spatial directions (that interact with transmission of momentum)

	The description of the equation will depend on which medium the water will be flowing since the acting forces will be described differently.		The description of the equation will depend on which medium the water will be flowing since the acting forces will be described differently.
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	So, the sum of the forces acting on surface waters:		So, the sum of the forces acting on surface waters:
−	[[Image:EqnQntMov ~~Forces~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov Forces1.png\|1000px\|thumb\|center\|]]

	And the complete set for momentum equation (St. Venant Equation in 1D or 2D):		And the complete set for momentum equation (St. Venant Equation in 1D or 2D):
−	[[Image:EqnQntMov ~~StVenant~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenant1.png\|1000px\|thumb\|center\|]]

	where:		where:
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	t: time		t: time
	H: Water column level = Channel/Topography Bottom level + water height		H: Water column level = Channel/Topography Bottom level + water height
−	x_i: spatial direction	+	x_i: spatial direction where velocity is solved
		+	x_j: all the spatial directions (that interact with transmission of momentum)
	g: gravity force (L.T-2)		g: gravity force (L.T-2)
	Sf: slope of the water surface or the linear hydraulic head loss (L/L)		Sf: slope of the water surface or the linear hydraulic head loss (L/L)

	And the same equation with flow (multiplied by vertical area):		And the same equation with flow (multiplied by vertical area):
−	[[Image:EqnQntMov ~~StVenantQ~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ1.png\|1000px\|thumb\|center\|]]

−	The ~~below~~ equation has to de discretized to space and time resulting in:	+	The above equation has to de discretized to space and time resulting in:
−	[[Image:EqnQntMov StVenantQ ~~discretization~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ discretization1.png\|1000px\|thumb\|center\|]]
	where:		where:
	t is the old value		t is the old value
	t+dt is the new value		t+dt is the new value
−	u subscript is from upstream	+	u subscript is from upstream (lower x_j)
−	d subscript is from downstream	+	d subscript is from downstream (higher x_j)

	And putting it relative to new flow <math>Q^{t+\Delta t}</math>:		And putting it relative to new flow <math>Q^{t+\Delta t}</math>:
−	[[Image:EqnQntMov StVenantQ ~~disc4_1step~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ disc4_1step1.png\|1000px\|thumb\|center\|]]
	where:		where:
−	[[Image:EqnQntMov StVenantQ ~~disc5~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ disc51.png\|1000px\|thumb\|center\|]]
−	[[Image:EqnQntMov StVenantQ ~~disc6~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ disc61.png\|1000px\|thumb\|center\|]]
−	[[Image:EqnQntMov StVenantQ ~~disc7~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ disc71.png\|1000px\|thumb\|center\|]]

	[Advection] and [Pressure] units are im L3.T-1 and [Friction] is adimensional. The remaining terms are defined above.		[Advection] and [Pressure] units are im L3.T-1 and [Friction] is adimensional. The remaining terms are defined above.

File:EqnQntMov StVenantQ disc71.png

2012-05-16T15:58:38Z

uploaded "[[File:EqnQntMov StVenantQ disc71.png]]"

File:EqnQntMov StVenantQ.png

2012-05-16T15:26:45Z

uploaded a new version of "[[File:EqnQntMov StVenantQ.png]]"

File:EqnQntMov StVenant1.png

2012-05-16T15:23:20Z

uploaded "[[File:EqnQntMov StVenant1.png]]"

File:EqnQntMov StVenant.png

2012-05-16T15:22:19Z

uploaded a new version of "[[File:EqnQntMov StVenant.png]]"

File:EqnQntMov Forces1.png

2012-05-16T15:18:47Z

uploaded "[[File:EqnQntMov Forces1.png]]"

File:EqnQntMov Forces.png

2012-05-16T15:16:46Z

uploaded a new version of "[[File:EqnQntMov Forces.png]]"

File:EqnQntMov Newton FixedVol.png

2012-05-16T15:15:01Z

deleted "[[File:EqnQntMov Newton FixedVol.png]]"

Mohid Bibliography

2012-05-12T13:05:08Z

← Older revision		Revision as of 13:05, 12 May 2012
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	Gomez-gesteira M, Montero P, Prego R, Taboada JJ, Leitão P, Ruiz-Villarreal M, Neves R, Pérez-Villar V. A two-dimensional particle tracking model for pollution dispersion in A Coruña and Vigo Rias (NW Spain). Oceanologica Acta. 1999; 22: 167-177. Available at: [[http://dx.doi.org/10.1016/S0399-1784(99)80043-7 Link]].		Gomez-gesteira M, Montero P, Prego R, Taboada JJ, Leitão P, Ruiz-Villarreal M, Neves R, Pérez-Villar V. A two-dimensional particle tracking model for pollution dispersion in A Coruña and Vigo Rias (NW Spain). Oceanologica Acta. 1999; 22: 167-177. Available at: [[http://dx.doi.org/10.1016/S0399-1784(99)80043-7 Link]].

−	Huhn F, von Kameke A, Allen-Perkins S, Montero P, Venancio A, Pérez-Muñuzuri V. Horizontal Lagrangian transport in a tidal-driven estuary—Transport barriers attached to prominent coastal boundaries. Continental Shelf Research. 2012; ~~In Press~~. Available at: [[http://dx.doi.org/10.1016/j.csr.2012.03.005 Link]].	+	Huhn F, von Kameke A, Allen-Perkins S, Montero P, Venancio A, Pérez-Muñuzuri V. Horizontal Lagrangian transport in a tidal-driven estuary—Transport barriers attached to prominent coastal boundaries. Continental Shelf Research. 2012; 39–40:1–13. Available at: [[http://dx.doi.org/10.1016/j.csr.2012.03.005 Link]].

	Huthnance JM, Coelho H, Griffiths CR, Knight PJ, Rees AP, Sinha B, Vangriesheim A, White M, Chatwin PG. Physical structures, advection and mixing in the region of Goban spur. Deep Sea Research Part II: Topical Studies in Oceanography. 2001; 48(14-15): 2979-3021. Available at: [[http://linkinghub.elsevier.com/retrieve/pii/S0967064501000303 Link]].		Huthnance JM, Coelho H, Griffiths CR, Knight PJ, Rees AP, Sinha B, Vangriesheim A, White M, Chatwin PG. Physical structures, advection and mixing in the region of Goban spur. Deep Sea Research Part II: Topical Studies in Oceanography. 2001; 48(14-15): 2979-3021. Available at: [[http://linkinghub.elsevier.com/retrieve/pii/S0967064501000303 Link]].
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	Fossati M, Piedra-Cueva I. A 3D hydrodynamic numerical model of the Río de la Plata and Montevideo’s coastal zone. Applied Mathematical Modelling. 2012; In Press. Available at: [[http://dx.doi.org/10.1016/j.apm.2012.04.010 Link]].		Fossati M, Piedra-Cueva I. A 3D hydrodynamic numerical model of the Río de la Plata and Montevideo’s coastal zone. Applied Mathematical Modelling. 2012; In Press. Available at: [[http://dx.doi.org/10.1016/j.apm.2012.04.010 Link]].

−	Huhn F, von Kameke A, Allen-Perkins S, Montero P, Venancio A, Pérez-Muñuzuri V. Horizontal Lagrangian transport in a tidal-driven estuary—Transport barriers attached to prominent coastal boundaries. Continental Shelf Research. 2012; ~~In Press~~. Available at: [[http://dx.doi.org/10.1016/j.csr.2012.03.005 Link]].	+	Huhn F, von Kameke A, Allen-Perkins S, Montero P, Venancio A, Pérez-Muñuzuri V. Horizontal Lagrangian transport in a tidal-driven estuary—Transport barriers attached to prominent coastal boundaries. Continental Shelf Research. 2012; 39–40:1–13. Available at: [[http://dx.doi.org/10.1016/j.csr.2012.03.005 Link]].

	Kenov IA, Garcia AC, Neves R. Residence time of water in the Mondego Estuary (Portugal). Estuarine, Coastal and Shelf Science. 2012; In Press. Available at: [[http://dx.doi.org/10.1016/j.ecss.2012.04.008 Link]].		Kenov IA, Garcia AC, Neves R. Residence time of water in the Mondego Estuary (Portugal). Estuarine, Coastal and Shelf Science. 2012; In Press. Available at: [[http://dx.doi.org/10.1016/j.ecss.2012.04.008 Link]].

Module PorousMedia

2012-05-11T13:24:26Z

Water Flow:

← Older revision		Revision as of 13:24, 11 May 2012
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	==Overview==		==Overview==
−	Module Porous Media is responsible for handling all water fluxes in soil~~. In particular the infiltration flow is obtained from the potential~~ water ~~column available for this process. The potential water column is given by~~ the ~~[[Module Basin]] (the module that handles interface~~ between ~~modules) as reported below:~~	+	Module Porous Media is responsible for handling all water fluxes in soil, including water transport due to the balance between pressure (gravity and suction) and resistance trough the medium, infiltration, evapotranspiration and link with the river (groundwater flow).
−		+	Soil fluxes are calculated by the Buckingham-Darcy equation (Jury et al,1991) and the connections with surface runoff and river are done using the same formulation where the surface water Head is the water level.
−	~~<math>PIC=TF+IWC</math>~~	+
−		+
−	~~where:~~	+
−	~~:{\|~~	+
−	~~\| ''PIC'' \|\| is the Potential Infiltration column~~ (m)	+
−	\|-	+
−	~~\| ''TF'' \|\| Throughfall is~~ the ~~percentage of~~ the ~~rain that reaches the soil~~ (m)	+
−	\|-	+
−	~~\| ''IWC'' \|\| is the Initial Water column (m)~~	+
−	\|}	+
−		+
−		+
−	~~The infiltration flux is~~ calculated by the Buckingham-Darcy equation ~~using head gradient between surface runoff and first soil layer~~ (Jury et al,1991).	+

	==Main Processes==		==Main Processes==
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	===Porous Media Geometry===		===Porous Media Geometry===
	Porous Media is a 3D domain delimited in its upper limit by topography and lower limit by soil bottom (defined by user).		Porous Media is a 3D domain delimited in its upper limit by topography and lower limit by soil bottom (defined by user).
−	In terms of soil definition it can be defined vertical horizons to ~~link~~ correspond to real soil horizons with different hydraulic carachteristics.	+	In terms of soil definition it can be defined vertical horizons to correspond to real soil horizons with different hydraulic carachteristics.
		+	See the picture blow for information.

	<htm><a href="http://content.screencast.com/users/jovem/folders/Jing/media/b9ef6c79-c1d1-46ea-94f7-623471c15883/MohidLandSoilProfile.png"><img src="http://content.screencast.com/users/jovem/folders/Jing/media/b9ef6c79-c1d1-46ea-94f7-623471c15883/MohidLandSoilProfile.png" width="650" height="436" border="0" /></a></htm>		<htm><a href="http://content.screencast.com/users/jovem/folders/Jing/media/b9ef6c79-c1d1-46ea-94f7-623471c15883/MohidLandSoilProfile.png"><img src="http://content.screencast.com/users/jovem/folders/Jing/media/b9ef6c79-c1d1-46ea-94f7-623471c15883/MohidLandSoilProfile.png" width="650" height="436" border="0" /></a></htm>

	===Water Flow===		===Water Flow===
−	Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation. In the case of soil it is assumed that ~~the forces of inertia~~ are ~~almost zero~~; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).	+	Soil contains a large distribution of pore sizes and channels through which water may flow. In general the water flow determination is based on the mass conservation and momentum equation [[Equations]]. In the case of soil it is assumed that acceleration is close to zero since velocities are very low; therefore the balance is reduced to the forces of pressure, gravity and viscous. The equation that describes the flow through soil is the Buckingham Darcy equation (Jury et al,1991).


−	<math>v=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial z} ~~\right )=-K\left ( \theta \right )\left ( \frac{\partial h}{\partial z} + 1~~ \right )\,\,\,\,(1.1)\\ </math>	+	<math>v=-K\left ( \theta \right )\left ( \frac{\partial H}{\partial x_i} \right )\,\,\,\,(1.1)\\ </math>

	where:		where:
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	\|-		\|-
	\| ''K''\|\| is the hydraulic conductivity (m/s)		\| ''K''\|\| is the hydraulic conductivity (m/s)
		+	\|-
		+	\| ''x_i''\|\| is direction i
	\|}		\|}

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	When in saturated conditions, hydraulic head is zero and hydrostatic pressure may occur (if water is at rest or decelerating). In unsaturated conditions hydrostatic pressure is zero and hydarulic head exists.		When in saturated conditions, hydraulic head is zero and hydrostatic pressure may occur (if water is at rest or decelerating). In unsaturated conditions hydrostatic pressure is zero and hydarulic head exists.

−	The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two ~~layers~~:	+	The soil is a very complex system, made up of a heterogeneous mixture of solid, liquid, and gaseous material. The liquid phase consists of soil water, which fills part or all of the open spaces between the soil particles. Therefore it is possible to divided the soil in two parts:


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	==Vadose Zone==		==Vadose Zone==

−	Many vadose flow and transport studies require description of unsaturated soil hydraulic proprieties over a wide range of pressure ~~head~~. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).	+	Many vadose flow and transport studies require description of unsaturated soil hydraulic proprieties over a wide range of pressure heads. The hydraulic proprieties are described using the porous size distribution model of Maulem (1976) for hydraulic conductivity in combination with a water retention function introduced by Van Genuchten (1980).

	===Water content===		===Water content===

Equations

2012-05-10T15:13:36Z

Surface Water (Runoff and Drainage Network):

← Older revision		Revision as of 15:13, 10 May 2012
(One intermediate revision by one user not shown)
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	u subscript is from upstream		u subscript is from upstream
	d subscript is from downstream		d subscript is from downstream
		+
		+	And putting it relative to new flow <math>Q^{t+\Delta t}</math>:
		+	[[Image:EqnQntMov StVenantQ disc4_1step.png\|1000px\|thumb\|center\|]]
		+	where:
		+	[[Image:EqnQntMov StVenantQ disc5.png\|1000px\|thumb\|center\|]]
		+	[[Image:EqnQntMov StVenantQ disc6.png\|1000px\|thumb\|center\|]]
		+	[[Image:EqnQntMov StVenantQ disc7.png\|1000px\|thumb\|center\|]]
		+
		+	[Advection] and [Pressure] units are im L3.T-1 and [Friction] is adimensional. The remaining terms are defined above.

	From St. Venant equations it is frequent to see simpler approaches used where acceleration is not accounted. In areas with slow varying slope and low Froudre number the horizontal velocity gradient is small and inertia forces can be neglected (Abbot and Minns, 1998). However the simplifications are more linked to low computation power or lack of numerical models to solve the full equations.		From St. Venant equations it is frequent to see simpler approaches used where acceleration is not accounted. In areas with slow varying slope and low Froudre number the horizontal velocity gradient is small and inertia forces can be neglected (Abbot and Minns, 1998). However the simplifications are more linked to low computation power or lack of numerical models to solve the full equations.

File:EqnQntMov StVenantQ disc7.png

2012-05-10T15:09:19Z

uploaded "[[File:EqnQntMov StVenantQ disc7.png]]"

File:EqnQntMov StVenantQ disc4 1step.png

2012-05-10T15:08:35Z

uploaded a new version of "[[File:EqnQntMov StVenantQ disc4 1step.png]]"

File:EqnQntMov StVenantQ disc4 1step.png

2012-05-10T15:06:55Z

uploaded "[[File:EqnQntMov StVenantQ disc4 1step.png]]"

Equations

2012-05-10T09:55:44Z

Surface Water (Runoff and Drainage Network):

← Older revision		Revision as of 09:55, 10 May 2012
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	The below equation has to de discretized to space and time resulting in:		The below equation has to de discretized to space and time resulting in:
−	[[Image:EqnQntMov StVenantQ ~~discretization2~~.png\|1000px\|thumb\|center\|]]	+	[[Image:EqnQntMov StVenantQ discretization.png\|1000px\|thumb\|center\|]]
	where:		where:
	t is the old value		t is the old value