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Mai Van Phu (riche)
New member Username: riche
Post Number: 1 Registered: 06-2006
| Posted on Tuesday, June 20, 2006 - 02:23 pm: | |
Hello Dr Nelson, I have an important question with Natural condition in Cylinrical Coordinates ('Z','R') with a axy-symetric geometric object. My equation to resolve is: curl(m*curl(A))-A=0 written in term of componants ( Ar, Atheta, Az). To obtain the NATURAL condition, I have used integration by part applied to the term curl(m*curl(A)). As result, the componant which correspond to Natural condition appears: Nartural componant: n x (m*curl(A))*2*pi*r With nr^2 + ntheta^2 + nz^2 = n^2 , n is the unit vector normal . So: Componant r: m*nz*(dAr/dr-dAz/dz) =... Componant theta: m*1/r* ( nz*(d(r*Atheta)/dz - nr*(d(r*Atheta)/dr) ) =... Componant z: m*nr*(dAr/dr-dAz/dz) =... My questions is that: What does mean NATURAL(..) in this case? In fact, we have not only one variable in (..), but Ar, Az or Atheta altogether . (usualy, we meet in other cases very simple, for example: Natural(Atheta)=… , which comes from: n*grad(Atheta) ) I have tried to set a new variable M= (dAr/dr-dAz/dz) and say: Value(M)=…. instead of Natural (dAr/dr-dAz/dz) ?? or something like that. But it doesn’t work. Could you help me Thank you so much. Riche.
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Robert G. Nelson (rgnelson)
Moderator Username: rgnelson
Post Number: 637 Registered: 06-2003
| Posted on Thursday, June 22, 2006 - 06:23 pm: | |
As pointed out in the documentation of Natural BC's, the Natural defines the value of the integrand of the surface terms arising from integrating second order terms by parts. Applied to the term curl(F), with F a vector, integration by parts yields the Curl Theorem Vol_Integral(curl(F)dV) = Surf_Integral(n x F)dS) So the meaning of the Natural of a curl equation is the value of the quantity (n x F) on the surface, applied componentwise to the component equations. This is directly compatible with Maxwell's equations, which require continuity of the tangential component of H at material interfaces.
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Robert G. Nelson (rgnelson)
Moderator Username: rgnelson
Post Number: 638 Registered: 06-2003
| Posted on Thursday, June 22, 2006 - 07:04 pm: | |
PS See our "Applications Manual" for more discussion of magnetic field problems. It is available for free download from our bookstore page at www.pdesolutions.com/bookstore.html
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Philip (riche)
New member Username: riche
Post Number: 2 Registered: 06-2006
| Posted on Thursday, July 27, 2006 - 01:39 pm: | |
Hello Dr Nelson, Thank you for your previous help since longtimes I have a question now about MESH EXPORT. I would like to transfer the SAME MESH of a file PDE ( after working of first file ) into another application of this file ( when I change a parameter in defintion). In other word, I want to save the mesh. I have tried 2 exemples: TRANSFER_out.PDE and TRANSFER_IN.PDE in the package "Applications Manual". But I find that they don’t give the SAME MESH. Finaly, I want to do a ratio of results between 2 applications, for exemple: (Elevation of Temp of first application / Temps of second). What can I do in this case. Maybe another command ? Thank you, Mai { This example uses a modification of the sample problem HEATBDRY.PDE to illustrate the use of the TRANSFER output function. Temperatures calculated here are transferred as input to the stress calculation TRANSFER_IN.PDE } title "Coolant Pipe Heatflow" Variables Temp(range=0,1) definitions K = 1 source = 4 Tzero = 0 flux = -K*grad(Temp) equations div(K*grad(Temp)) + source = 0 boundaries Region 1 natural(Temp)=0 start "OUTER" (0,0) line to(1,0) natural(Temp)=0 arc (center=0,0) to (0,1) natural(Temp)=0 line to finish natural(Temp)=Tzero-Temp start "INNER" (0.4,0.2) arc (center=0.4,0.4) to (0.6,0.4) to (0.4,0.6) to (0.2,0.4) finish monitors contour(Temp) plots grid(x,y) contour(Temp) surface(Temp) vector(-K*dx(Temp),-K*dy(Temp)) as "Heat Flow" contour(source) elevation(normal(flux)) on "outer" range(-0.08,0.08) report(bintegral(normal(flux),"outer")) as "bintegral" elevation(normal(flux)) on "inner" range(1.95,2.3) report(bintegral(normal(flux),"inner")) as "bintegral" { HERE IS THE TRANSFER OUTPUT COMMAND: } transfer(Temp) file="transfer.dat" end 15317 { This problem demonstrates the use of the TRANSFER facility to import temperatures from TRANSFER_OUT.PDE as the source of thermal expansion driving a stress calculation. TRANSFER_OUT.PDE must be run before running this problem. } Title 'Testing the TRANSFER input function' select painted { paint all contour plots } variables U V definitions nu = 0.3 { define Poisson's Ratio } E = 21 { Young's Modulus x 10**-11 } G = E/(1-nu**2) C11 = G C12 = G*nu C22 = G C33 = G*(1-nu)/2 alpha = 1e-3 b = G*alpha*(1+nu) { HERE IS THE TRANSFER INPUT FUNCTION: } transfer('transfer.dat',Temp) Sxx = C11*dx(U) + C12*dy(V) - b*Temp Syy = C12*dx(U) + C22*dy(V) - b*temp Sxy = C33*(dy(U) + dx(V)) initial values U = 0 V = 0 equations dx[Sxx] + dy(Sxy) = 0 dy[Syy] + dx(Sxy) = 0 constraints integral(u) = 0 integral(v) = 0 integral(dx(v)-dy(u)) = 0 boundaries Region 1 start "OUTER" (0,0) natural(U)=0 value(V)=0 line to(1,0) natural(U)=0 natural(V)=0 { free outer boundary } arc (center=0,0) to (0,1) value(U)=0 natural(V)=0 line to finish natural(U)=0 natural(V)=0 { free inner boundary } start "INNER" (0.4,0.2) arc (center=0.4,0.4) to (0.6,0.4) to (0.4,0.6) to (0.2,0.4) finish monitors grid(x+100*U,y+100*V) plots contour(Temp) grid(x+100*U,y+100*V) vector(U,V) as "Displacement" contour(U) as "X-Displacement" contour(V) as "Y-Displacement" contour(Sxx) as "X-Stress" contour(Syy) as "Y-Stress" surface(Sxx) as "X-Stress" surface(Syy) as "Y-Stress" end 5535
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Robert G. Nelson (rgnelson)
Moderator Username: rgnelson
Post Number: 665 Registered: 06-2003
| Posted on Friday, July 28, 2006 - 01:38 am: | |
Any TRANSFER output writes all the mesh data. On input, TRANSFER creates a secondary mesh in which the input data can be interpolated. It does not map the input mesh onto the computation mesh. In order to force FlexPDE to use the imported mesh as the computation mesh, you must import using the TRANSFERMESH command. See all the TRANSFER... listings in the Help Index.
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Philip (riche)
Member Username: riche
Post Number: 4 Registered: 06-2006
| Posted on Monday, July 31, 2006 - 07:40 am: | |
Dr Nelson, I am using flex PDE version 2.20d 3D. I can use tranfer but not transferMESH. I think that my problem is here. So, can I resolve it. Thank you for your help. Best Regard, Mai |
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