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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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