| Author | Message | ||
     Mark Flegg (z_wasa) New member Username: z_wasa Post Number: 1 Registered: 10-2005 |
I have a question regarding the equation that I use and how the natural boundary condition is generated from it. I have two regions, the first has the value of say v as 0 and the other has the value of v as 1. The PDE looks something like (ommiting constants and things like that)... dzz(H)+v*H+(1-v)*dz(H)=0 What happens here over the boundary if I say make natural(H)=0. is the only thing that effects this boundary condition the dzz term? does this mean that it will match the value and derivative over the boundary? Thanks heaps! | ||
| Mark Flegg (z_wasa) New member Username: z_wasa Post Number: 2 Registered: 10-2005 |
Oh and another thing with this! if it is not the case that it will match the derivative and the value at this point, is there anyway for me to make it do so. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 471 Registered: 06-2003 |
Natural boundary conditions are discussed in several places in the documentation. See "Natural" in the Help Index. Quickly summarized: FlexPDE integrates second-order derivative terms by parts. This gives rise to boundary terms. These boundary terms comprise the Natural boundary condition at outer boundaries, and define the continuity conditions at interior boundaries. In your case, the surface term arising from dzz(H) is dz(H). This term is assumed continuous across interior boundaries. That is, no surface term is computed at interior boundaries, so continuity of the derivative is built in to the discretization. You omitted constants and things, but be aware that in the term dz(K*dz(H)), it is K*dz(H) that is continuous, not dz(H). Values are continuous by default, since the mesh nodes are shared between adjoining cells. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 472 Registered: 06-2003 |
PS Natural(H)=0 is the default, interior or exterior, so you don't need to specify Natural(H)=0 on any boundary, but particularly on interior boundaries. If you specify Natural(H) different from zero on an interior boundary, it represents a line source. |