| Author | Message | |||
     Jerome Jonnet (tintin) New member Username: tintin Post Number: 1 Registered: 02-2004 |
Hi, I am trying to solve biharmonic equations with a source term, defined by a wall of Dirac ... In a first try, I only used UPULSE, but it appeared that the source was not very well defined for the solution ... So, in a second try, I defined different cells, in which one of the boundary is located directly in the wall of Diracs ... but now, I think I have a problem of boundary conditions ... The solution is then null (like there was no source ) !!! Has someone already had this problem ??? Thank you very much !
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 191 Registered: 06-2003 |
In your PDE, Q is a volume source. But your definition of Q is nonzero only along two lines; there is no volume in which Q is nonzero. Therefore, there is no source. If you want Q to act as a boundary load, then you must impose it as a boundary term. A Natural BC on an internal boundary is a source (or sink). It is the difference between the boundary "fluxes" on the two sides of the boundary. In your problem, Natural(psi) is the outward normal derivative of psi, while Natural(pso) is the outward normal derivative of pso. Decide how Q is supposed to act on these equations, and put it in as the appropriate Natural. An example of this kind of thing is the electrostatic equation div(eps*grad(V))=rho. An interior natural(V) means a surface charge. This follows directly from the definition of the Natural BC. In your case, an internal Natural(psi) is probably a line load, but check the arithmetic before taking my word for it. | |||
| Jerome Jonnet (tintin) New member Username: tintin Post Number: 2 Registered: 02-2004 |
Yes, you're right ! I have tried, and there is a solution ... but I have done it by defining the source on the (external) boundaries. Do you know how I can define an internal one ??? Thank you ! | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 192 Registered: 06-2003 |
You can define a Natural() boundary condition on an internal boundary. | |||
| Jerome Jonnet (tintin) Junior Member Username: tintin Post Number: 3 Registered: 02-2004 |
Is that correct ? The internal boundary condition is defined in REGION 2 ... Boundaries Region 1 start (0,0) natural(psi) = 0 natural(pso) = 0 line to (10,0) natural(psi) = 0 natural(pso) = 0 line to (10,5) natural(psi) = 0 natural(pso) = 0 line to (0,5) natural(psi) = 0 natural(pso) = 0 line to finish Region 2 start (0,1) line to (10,1) natural(psi) = 0 natural(pso) = Q line to finish Thanks a lot ... | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 193 Registered: 06-2003 |
Your region 2 has no volume. FlexPDE assumes that a "region" has an enclosed volume. If you merely want to put in a line that does not bound a material region, use "feature" instead of "region". With that change, your script will apply a surface source Q units per unit distance on the stated boundary. If Q was your source per unit area, you will probably have to do something to it to make the units correct. |
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