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Olivier Lami (ol9245)
Junior Member
Username: ol9245

Post Number: 3
Registered: 04-2005
Posted on Wednesday, April 13, 2005 - 05:54 am:   

Hi all,

This is a free surface flow problem.
H is the water depth
u and v are the flow velocity in both directions.

the water can get out of the plot only by the bottom end of the plot.

for the closed boudaries, either of the followings work fine :
natural(H)=0
or
value(u -or v, whichever is relevant-) = 0

for the open boudary, where the flow must come out, the boundary condition I want is to set the free surface parrallel to the ground.

I tried the followings
value (dy(H)) = 0
value (dx(v)) = 0

but none of them were understood by FlexPDE.

any help would be highly appreciated to fix this.
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Victor Bense (indiana)
New member
Username: indiana

Post Number: 2
Registered: 01-2005
Posted on Wednesday, April 13, 2005 - 11:55 am:   

Hi,

I think you should try to set the natural boundary condition as being equal to the flux over the boundary. Something like:

natural(H)= Q

where Q is calculated using darcy's law for example.

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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 351
Registered: 06-2003
Posted on Wednesday, April 13, 2005 - 02:48 pm:   

If you read the documentation, you will learn that the Natural boundary condition is given its meaning by integrating the second-order terms of the PDE by parts (divergence theorem).

There are no second order terms in your equations, so the Natural BC is undefined.

First-order equations need and are allowed one boundary condition on each flow path, necessarily at the incoming end. Because the Natural is undefined, you must provide a Value.

Alternatively, you can use the option SELECT FIRSTPARTS, which will cause first-order terms to be integrated by parts. In this case, the Natural will be defined by the first-order terms.
The Natural BC for the H equation will then be the outward surface-normal component of the vector (Qx,Qy).

I suggest again that you use a stream-function approach. See the examples "Airfoil.pde" and "Buoyant.pde" in the "SAMPLES | Steady_State | Fluids" folder.
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Olivier Lami (ol9245)
Member
Username: ol9245

Post Number: 4
Registered: 04-2005
Posted on Wednesday, April 13, 2005 - 03:56 pm:   

Hi all,

Thanks for helping.

Yes I have read some of the doc. Unfortunately, a significant part of it is far beyond my math skills. However, I still trust in my ability to solve this problem, provided some kind help and hints. Thanks again about that.

I have seen the airfoil.pde, which looks the closest example to my problem. In airfoil.pde, the input and output fluxes are (i) known and (ii) uniform over the boundary.

Therefore I cannot do things as simple as they are in airfoil.pde. The reason is because I deal with a free surface flow. Thus my output flux is :
(i) unknown because the volume of water stored at the soil surface may vary in time.
(ii) not uniform : the water flux depends on the local soil topography.

in a previous resolution of this problem I have done with finite difference method, I have added dummy cells at the outlet and force these cells to have the same water depth H than the ones at the border.

How can I translate this BC in FlexPDE logic ?

Thanks for helping

application/octet-streamprogram
SaintVenant time dependent.pde (2.4 k)


application/octet-streamsurface
simplesmall.dat (1.0 k)
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Gilson Gitirana Jr (ggitirana)
Member
Username: ggitirana

Post Number: 5
Registered: 11-2003
Posted on Sunday, April 17, 2005 - 08:49 pm:   

Hi,
I'm not sure I understand your BC, but I'll try to help:

Here's the symbols I'll use: H is head, Uw is pore-water pressure, gw is unit weight of water.. H = uw/gw + y

Now the B.C.'s:

VALUE(H) = Y would give a fixed value for H, corresponding to Uw = 0.
This BC corresponds to a free surface where no ponding is allowed.

If you have a surface were water may or may not be flowing through (i.e., you don't know the exit point), you have to using something diferent:

NATURAL(H) = if (H-y)*gw<0 then 0 else -H*LARGENUMBER

Translation: if uw is negative, no flow, if uw get positive, apply a large flow to remove this water and return Uw to 0.

You have to use an appropriate hydraulic conductivity function to have meaningful results in terms of flow in unsaturated areas.

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