boundary conditions with pdepe when m>0

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Nicholas Mikolajewicz 2018-1-29

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评论： Nicholas Mikolajewicz 2018-1-30

Hello,

I'm trying to simulate a 2d diffusion problem where the source at the boundary is time-dependent. I have no problem imposing this boundary conditions when m=0 (i.e., problem is in 1 dimension), but as soon as I try to run the simulation in 2 dimensions (m=1), it doesn't work.

In the pdepe documentation I found the following that pertains to my problem:

When m > 0 and a = 0, boundedness of the solution near x = 0 requires that the flux f vanish at a = 0. pdepe imposes this boundary condition automatically and it ignores values returned in pl and ql.

thus, my time-dependent source is ignored entirely when m=1. Is there any work around to this? Is there anyway to use the 1d solver to simulate the 2d problem?

Thanks

Nick

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采纳的回答

Torsten 2018-1-30

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Setting m=1 does not make your computation 2-dimensional, but calculations are done over the radius of a cylinder. You can't prescribe a source at the axis of a cylinder (x=0) because the area over which this source would be added is zero.

Best wishes

Torsten.

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Torsten 2018-1-30

I don't know your experimental set-up. So I can't say whether it is legitimate to use a 1d-model to reproduce your experimental results.

E.g. if you have a cylinder which is heated at r=R with a constant heat flux over the height, it is legitimate to model the temperature over the radius as an 1d-problem using "pdepe".

If the heat flux is not constant over the height, you will have to set up the problem 2-dimensional (radius and height as independent variables).

Best wishes

Torsten.

Nicholas Mikolajewicz 2018-1-30

the source height is approximately 20 micrometers while the height of medium is 3 millimeters...so I suppose 2d is more appropriate... This can all be achieved using the pde toolbox?

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