| Author | Message | ||
     Charles Crapuchettes (chuckc) New member Username: chuckc Post Number: 1 Registered: 10-2009 |
I'm using FlexPDE 5.1.4 Solving an RF plasma problem, using the simplifying assumption that the charge on the surfaces facing the plasma does not vary much during the RF cycle (compared to RF current) so can be pretended to be constant. The potentials at 2 times in the RF cycle are modeled using equations: u1: div(er*grad(u1))=q1 u9: div(er*grad(u9))=q9 with q1 and q2 being complicated functions of u1 and u9. Along the plasma boundary I would like to be able to do something equivalent to the (illegal) syntax: value(u9) = -10 natural(u1) = natural(u9) I think the legal syntax that should do what I need along the boundary is: value(u9) = -10 natural(u1) = jump(normal(er*grad(u9))) or possibly value(u9) = -10 natural(u1) = jump(normal(-er*grad(u9))) However, FlexPDE reports "illegal item encountered on input" with the "normal" highlighted. It seems to me that this should work, because nothing in the manual regarding "jump" puts any restrictions on the argument for jump. So, I'd think it would accept a scalar expression of any complexity involving any number of variables. Since that seems to not be the case, what are the restrictions on the argument of the jump function? If I can't use jump to do what I need to do, how can I do what I need to do? I can't see, for example, how to separately get the normal component of a vector on the inside and outside of the boundary, so I could subtract them. Note that in this particular problem, there are several other variables representing different times in the RF cycles, which act similarly to u1 above. On some parts of the boundary, like above, u9 gets a value conditions, and all others get natural conditions. On other parts of the boundary, it is u1 that gets the value condition and all others get natural conditions like u1 did above. On other parts of the boundary, all have nobc conditions. On other parts, all have value conditions. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1297 Registered: 06-2003 |
1. "NATURAL" is a boundary condition selector, and cannot be used as an arithmetic value. But since NATURAL(u9) defines the normal derivative of er*grad(u9), you can use the expression NORMAL(er*grad(u9)) as the right-hand-side of the NATURAL(u1) definition: NATURAL(u1) = NORMAL(er*grad(u9)) This will have the effect that you indicate as NATURAL(u1)=NATURAL(u9). 2. While the documentation is not terribly explicit about the point, it does say: ---------------------------- JUMP(v) means the instantaneous change in the value of variable 'v' when moving outward across an interface from inside a given material. ----------------------------- The implication and the fact is that JUMP can only take VARIABLES as arguments, since it is the discontinuity in the variable that is the controlling factor in CONTACT boundary conditions. JUMP has no meaning unless it is applied on a boundary that has been declared as a CONTACT boundary, because it is only at these boundaries that variables are not forced to be continuous across the interface. | ||
| Charles Crapuchettes (chuckc) New member Username: chuckc Post Number: 2 Registered: 10-2009 |
Thank you, but what I need is not NORMAL(er*grad(u9)), it is the change in NORMAL(er*grad(u9)) across the boundary. I don't see a way to specify that in a boundary condition, other than by using jump, which doesn't work. Note that NORMAL(er*grad(u9)) is discontinuous across the value(u9) boundary condition. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1298 Registered: 06-2003 |
Since in the absence of Value or Natural BC's, Normal(er*grad(u9)) will be continuous (no jump), it follows that what you want to know is the amount of flux injected in holding u9 at the specified value. One way to observe this value would be to use a NATURAL(u9) to inject flux and run a STAGED problem varying the amount. Plot a history of this quantity and of u9 at the boundary and pick off the flux at the point where u9 crosses -10. The only way I can think of to apply this value automatically into another equation is to define an additional variable that is the value of er*grad(u9)<dot>direction and apply a CONTACT BC with large resistance to dissociate the values of this variable on the two sides of the interface. Then you can use JUMP(new variable) in the BC for u1. There may be other ways to address this problem, but without knowing more about what the physical process is that causes this coupling, I can't guess. | ||
| Charles Crapuchettes (chuckc) Junior Member Username: chuckc Post Number: 3 Registered: 10-2009 |
The physical mechanism is surface charge that is applied to the surface during the RF cycle. The surface charge comes from the plasma. The ion current is constant and independent of the voltage, the electron current only flows at the part of the cycle with the more positive voltage, and is very sensitive to voltage. The DC charge on the surface is controlled by the part of the cycle with the higest voltage, but for different parts of the surface the control is at differnt times in the RF cycle, and the amount of charge varies along the surface depending on the electric fields through the surface. Surfaces are generally insulators, with some that are semiconducting or metal. |