Need help finding the right PDE coefficients of this equation

Hi everybody,

I can't figure out what are the coefficients of this equation in comparison with PDE toolbox parabolic equation format, any suggestion is really appreciated:

or its tensor equivalent:

Theta is a scalar and the domain is in x-z plane.

thanks,

Mohammad,

[Bill Greene]

I might be able to suggest something but I don't understand either version of your equation.

In the first equation, what is del(z)? Is that the vector (0,0,1)? Isn't div(del(z)) equal zero?

In the second version, what is h? What are the ranges for i and j for the 2D PDE Toolbox case? 1->2 or 1->3?

Beyond those questions, could you be more specific about where you are stuck?

Bill

[Mohammad Monfared]

Let's focus on the first equation: yes del(z) is (0,0,1) [or in my case in 2-D is (0,1)] and the second term of right side of equation becomes:

 div(-K*del(z)) = -K*div(del(z)) + div(-K)*del(z) = div(-K)*del(z)

as I mentioned in my previous posts, you know, my problem is in declaration of the 'a' coefficient. 'a' is a vector here but theta just a scalar.

Mohammad

[Bill Greene]

OK. I believe there must be a problem with the equation. Obviously, d(theta)/dt is a scalar. So the terms on the RHS must be scalars too. The term div(-K)*del(z) just doesn't fit with the rest of the equation.

Bill

[Bill Greene]

Sorry, I forgot to mention that the term we are talking about is the "f" coefficient-- not the "a" coefficient in PDE Toolbox terminology. "a" is zero in your case because you don't have a term multiplying theta. Like "a", "f" also must be a scalar. But if the purpose of del(z) is simply to extract a scalar term from K, just set "f" to that scalar and you should be all set.

Bill

[Mohammad Monfared]

Now I have better understanding of my equation. " div(-K)*del(z) " is a scalar itself so no problem with that anymore. Since K is a function of theta and d(K)/d(z) and hence, d(K)/d(theta) . d(theta)/d(z) is to be determined, there is a need to know theta at each node to complete the task, so it seems to me the right choice should be 'a' not 'f'.

a new question came to me: while assigning Neumann boundary conditions, the general form is:

 n.(c*del(u)) + q*u = g

now what if 'c' in boundary condition differs from 'c' in the main PDE equation (which is my case)?

with appreciation,

Mohammad

[Mohammad Monfared]

please ignore my new question from my previous comment.