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Marc Zwaanswijk (marcz)
New member
Username: marcz

Post Number: 2
Registered: 11-2004
Posted on Wednesday, December 08, 2004 - 11:01 am:   

Hi Flex-users,

In my 2D rectangular model I want to vary the pressure with depth as function of the density at my right and left boundary. Therefor I have to use an integration definition in FlexPDE to define the attached problem. I already used line_integral, but it doesnt give right results.
Does anybody know how to define such boundary conditions in Flex? Maybe it helps to note that my density is defined by: rho=1000*exp(0.69*omega) where omega is my concentration variable.

Hopefully someone can help me
Thanks a lot,
greetz Marc

application/mswordIntegration problem
integral.doc (15.9 k)
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 277
Registered: 06-2003
Posted on Wednesday, December 08, 2004 - 04:12 pm:   

1.
I don't understand your integral. Your limits are values of y, rho is a function of y, but the integration variable is z. How does z relate to y?

2.
You haven't given enough information about your system. You refer to this as a boundary condition, but it would appear to be an interior variable. How about a full discription of the problem.

3.
How about making pressure another variable?
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Marc Zwaanswijk (marcz)
Junior Member
Username: marcz

Post Number: 3
Registered: 11-2004
Posted on Thursday, December 09, 2004 - 03:38 am:   

Mr Nelson,

Thank you for looking at it. I will give you more information.

1. z=y. I made a typing mistake. The integration variable is ofcourse y too.

2. My system describes three horizontal hydro-geologic layers. In this system I want to simulate solute transport of groundwaterflow. I have two variables: 1) pressure (which is a function of the density and 2)omega (the salt concentration which influences the density).
The base boundary is closed: natural(pressure)=0, the upper boundary is defined by: value(pressure)=0. Now the pressure in the interior must be defined by the attached integral: The pressure will depend on the depth (y) and density.
I tried to use a line_integral on the left and right boundary but that didnt give right results.

3) Same problem for my second variable omega. The concentration omega also depends on the depth (y) by the following formula: omega=2.14e-3*erf(y/(8/3)). It states that omega is close to 2.14e-3 for y=8 till y=32 (baselevel)

Now the problem is to find a way to define these conditions of pressure and omega to the whole interior of my system.
I hope this will enough information and I hope that you will find a way to help me with this.
Thanks again,
Marc

application/mswordProblem Integral
integral.doc (15.9 k)
text/plainSystem script
Lichtaard2D-3.pde (3.2 k)

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