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Neumann Boundary Conditions

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Neumann Boundary Conditions

Hello folks,

I'm trying to learn how to specify Neumann boundary conditions using numol to solve a PDE.

As you may be aware, Prime 3.0 does not feature Pdesolve so if we want to solve a PDE, we need to use either numol, relax or multigrid.

I'm using a rather simple example of Pdesolve in which we have a flat plate perfectly insulated at x=0 and with convection at x=L.

Now, the problem I'm having is that I cannot decipher how to express these boundaries conditions when using numol.

If someone knows how to do this, please solve the problem in the attached file using numol and post the solution in the reply.

Thanks a lot for you help!

P.S.: I saved the file in Mathcad 11 format so that a bigger audience may be able to open it and contribute. Thanks again.

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Neumann Boundary Conditions

Try this. I did it in MC 15 so I could read your model easily but it should work the same in Prime.

6 REPLIES 6

Re: Neumann Boundary Conditions

I looked at your pdesolve example and your second boundary condition is called "mixed", not Neumann, because it involves both the dependent variable and its derivative. Numol does not accept mixed boundary conditions. That is why we need pdesolve back in Prime, but hopefully in a vector/matrix form.

Re: Neumann Boundary Conditions

Thanks Harvey for your reply.

Now, if we change the second boundary condition to a true Neumann BC, say, a heat flux of 5. How do we set up the boundary conditions?

The example that is included in the Mathcad 15 help is, in my opinion, confusing, at least in terms of the boundary conditions.

Thank you again.

Re: Neumann Boundary Conditions

Try this. I did it in MC 15 so I could read your model easily but it should work the same in Prime.

Re: Neumann Boundary Conditions

I think I had the init argument wrong, so an updated file is attached. It doesn't change the results because the init values are not a function of x.

Re: Neumann Boundary Conditions

Oops. The x and t arguments were still incorrect in places. But because of your problem, nothing changed.

Re: Neumann Boundary Conditions

Harvey, thanks a lot!

Yes, I noticed the minor issue with the argument of bc_func, but that much I knew how to figure out. As you mentioned, the result is unaltered as the slab is initially at a constant temperature.

Pdesolve is DEFINITELY needed in Prime as numol is not quite as versatile as pdesolve (not that pdesolve is perfect, but considering...).

Anyway, thanks again.

Best,

Josué