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Serge-Étienne Parent (dernier_recours)
New member
Username: dernier_recours

Post Number: 1
Registered: 04-2005
Posted on Monday, April 11, 2005 - 05:45 pm:   

Hi,

I'm trying to figure out these days how FlexPDE works. For now, I would like to model pressure and flow through a soil column submitted to precipitations. How can I add a NATURAL and time-dependant boundary condition (for example, a weekly precipitation matrix) to the richards.pde problem?

Thanks!
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 349
Registered: 06-2003
Posted on Monday, April 11, 2005 - 07:20 pm:   

Richard's equation, as I am familiar with it, says
dx(k*dx(h))+dy(k*(dy(h)+1)) = C*dt(h)

FlexPDE documentation of Natural Boundary conditions applied to this equation says that the Natural BC specifies the outward normal component of the vector [K*dx(h), K*(dy(h)+1)].

So, you put into the Natural BC the values you want for this quantity. This can be a time-dependent expression.
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Gilson Gitirana Jr (ggitirana)
Member
Username: ggitirana

Post Number: 4
Registered: 11-2003
Posted on Tuesday, April 12, 2005 - 11:19 am:   

Mr. Nelson's PDE is correct, but he's using a symbol that may be confusing. Here's how you can do it:

The PDEs:
dx(k*dx(h))+dy(k*(dy(h))) = C*dt(h)
or
dx((k/gw)*dx(uw))+dy(k*(dy(uw/gw))+1) = C*dt(uw)
h is total head, uw is pore-water pressure

Precipitation can be entered with the TABLE function, making t the first variable and precipitation the second. If you have simple data, you could also use the if command.
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Serge-Étienne Parent (dernier_recours)
New member
Username: dernier_recours

Post Number: 2
Registered: 04-2005
Posted on Tuesday, April 12, 2005 - 03:21 pm:   

Hi,

My math classes are far away and were not a great success indeed. In every forms of unsaturated flow PDE I have seen in the litterature, a source/sink term appears. For example:

C*dt(h)= div(k*grad(y+h))+Q

where y is elevation, h is pressure <total_head=y+h> and Q is the source/sink term.

1- I have always thought that this term meant the envetual flow boundary condition. Am I right?
2- If not, how the natural b.c. should be written into FlexPDE?
3- If I write NATURAL(h)=1, does that mean that the vector [K*dx(h), K*(dy(h)+1)] equals to [1,1] on the boundary?

Thanks,

S.É.P.

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