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f. e. k. (faysal)
New member
Username: faysal

Post Number: 1
Registered: 03-2007
Posted on Friday, March 02, 2007 - 04:45 pm:   

Hello,

I have to resolve a coupled equations:

equations

L: div( k*grad(L) - k_i*grad(L_i) ) = 0
L_i: div( k*grad(L_i) + k_i*grad(L) ) = 0

with a Natural conditions

k*Natural(L)- k_i*Natural(L_i) = givenvalue1
k*Natural(L_i) + k_i*Natural(L) = givenvalue2

FlexPde is not allowing me the mixing.

Any idea?

Thanks.

F.
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 775
Registered: 06-2003
Posted on Friday, March 02, 2007 - 06:45 pm:   

"Natural" is not a function. It is a boundary condition declarator.
The only thing you get to say is
Natural(var)=something.

In your system, Natural(L) provides the value of the outward normal component of K*grad(L)-k_i*grad(L_i) [Divergence theorem].

I assume that what you want is merely
Natural(L) = givenvalue1
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f. e. k. (faysal)
New member
Username: faysal

Post Number: 2
Registered: 03-2007
Posted on Monday, March 05, 2007 - 02:32 pm:   

I will be more clear:

Div( k + i*k_i) ( L + i*L_i)) = 0

is our complex equation, the conductivity is assumed a complex number, then the potential is a complex function L + i*L_i,(two variables).


Real Part: div( k*grad(L) - k_i*grad(L_i) ) = 0

Imaginary Part: div( k*grad(L_i) + k_i*grad(L) ) = 0

Boundary condition is:


( k + i k_i) d( L + iL_i))/dn = (givenvalue1 i*givenvalue2)

it comes too:

K*dL/dn- K_i*dL_i/dn = givenvalue1
K_i*dL/dn+ K*dL_i/dn = givenvalue2


Now how we can express this boundary conditions in FlexPDE.

If I understand you well,

natural(L) =givenvalue1 is equivalent to K*dL/dn- K_i*dL_i/dn = givenvalue1

natural(L_i) =givenvalue2 is equivalent to K_i*dL/dn+ K*dL_i/dn = givenvalue2

Is my understanding corect?

thank you very much,
Faysal.
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 777
Registered: 06-2003
Posted on Monday, March 05, 2007 - 04:17 pm:   

The Divergence Theorem says
Vol_Integral(Div(Vector))=Surf_Integral(normal<dot>Vector)

The NATURAL boundary condition supplies the integrand for the Surf_Integral, namely
normal<dot>Vector.

So your interpretation is exactly correct.

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