| Author | Message | ||
     Kyle (kyle) Member Username: kyle Post Number: 14 Registered: 08-2006 |
Hi Robert: Regarding your Dec. 4, 2006 post, issue 3: The FlexPDE 5.0 Reference Manual p.84 indicates that if no BC is given for a region, then the BC Natural(u)=0 is assumed. This means, for the case of diffusion equation, the flux [-(D_Region)*normal(grad(u))] is zero rather than conserved across an internal boundary if a subregion is made without giving BCs. I don't think FlexPDE is really setting the flux to zero as the Reference Manual specifies. Can you please elaborate? Thank you very much, Kyle | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 716 Registered: 06-2003 |
The Divergence Theorem applied over an area says that the area (or volume) integral of a divergence is equal to the surface integral of the normal component of flux across the bounding surface. This normal flux is what is defined by the NATURAL() statement in FlexPDE. If you combine two areas, each integrated by the Divergence Theorem, the surface component in area 1 due to the shared boundary exactly cancels the corresponding term in the second area, so that the total integral has zero contribution from the shared boundary. This is what NATURAL()=0 means on an interior boundary. There is no net contribution to the integral. If NATURAL() is NOT zero on and interior boundary, this implies an interior surface source or sink. On an OUTER boundary, which is not cancelled by an adjoining region, NATURAL()=0 means NO FLUX, just as stated in the documentation. Strictly speaking, an interior "boundary" is not a "boundary" at all, in the sense that it does not "bound" the domain. |