| Author | Message | ||
     Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 5 Registered: 08-2003 |
The condition Dtangential(A)=0 is the same than (n x grad(a))=0? Where n is the normal versor to boundary surface. If I´ve the following PDE div(grad(A))+ k*A= F To deduce the natural(A)=v boundary condition I integrate by parts the first term only ,then is equivalent to grad(A) . n =v . That´s right? Thank you very much. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 21 Registered: 06-2003 |
Dtangential(A) specifies the value of (n x grad(A)). (n x Vector) is the natural boundary condition for the PDE term curl(Vector). The PDE term div(grad(A)) generates a surface term n.grad(A), as you state. The Natural BC for this term provides the value of n.grad(A). See the Help sections "Technical Notes | Natural Boundary Conditions" and "User Guide | Addressing More Difficult Problems | Natural Boundary Conditions". There are implementation problems with Dtangential and Dnormal which make the Natural BC much preferable. 1) Dnormal and Dtangential are applied at mesh nodes, which creates an ambiguity about what condition is to be applied at a corner. Natural BCs are by implication integrals over a mesh leg, and therfore do not conflict with nodal conditions at corners. 2) in some geometries the Dtangential and Dnormal specifications can reduce to 0/0. | ||
| Patricio A. Greco (pagreco) Member Username: pagreco Post Number: 6 Registered: 08-2003 |
If Dtangential(A) is different to 0 then , as is equivalent to n x grad(A). I´ve a couple of questions: 1) if n=(nx,ny,nz) nx^2+ny^2+nz^2=1 ? 2) the result of n x grad(A) in a vector how can I define each component at the bondary surface. Suppose I´ve a plane surface in the x,y plane then nx=ny=0 ,nz=1, n x grad(A)=(-dy(A),dx(A),0), How can I define the value for each component. Thank you very much. |