| Author | Message | |||
     Alexander Kalinin (alkalinin) New member Username: alkalinin Post Number: 1 Registered: 10-2005 |
In my sample task (3d_sphere.pde, see attachement) I assign the natural boundary conditions as "surface 1 natural(u) = 1.0" But, I don't understand one moment. The natural boundary conditions can be assigned on interior side as well as on exterior side of surface. So, which side of surface (interior or exterior) belongs natural conditions in the "surface 1 natural(u) = 1.0" expression? And how FlexPDE determines the side of surface, along z axis or another way?
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 474 Registered: 06-2003 |
There is extensive discussion of Natural boundary conditions in the FlexPDE documentation. See "Natural" in the Help Index. Briefly summarized: The finite element method forms equations at discrete nodes by integrating the weighted PDE over the cells surrounding each node. FlexPDE integrates second derivative terms by parts (equivalent to the divergence theorem in appropriate circumstances). This creates surface terms as part of the integral. These surface terms define the outward normal flux at exterior boundaries, or the "out-in" flux imbalance at interior boundaries. You do not apply boundary conditions on both sides of an interface. You do not apply boundary conditions on the outside of an exterior boundary. There is no computation outside the domain. In your sample problem, you have specified a natural BC of 1 on the bottom of the sphere. According to the definition of natural boundary conditions, this means an outward flux of one unit across the bottom hemisphere. This is exactly what your plot shows. | |||
| Alexander Kalinin (alkalinin) New member Username: alkalinin Post Number: 2 Registered: 10-2005 |
I see. Thank you very much. |
3d_sphere