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Shell diffusion solution not satisfying the governing PDE - Problem with tangential derivatives
Posted 19 gen 2015, 22:06 GMT-5 Modeling Tools & Definitions, Parameters, Variables, & Functions 0 Replies
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In an attempt to further study tangential derivatives, I was working with the shell diffusion model available here:
www.comsol.com/model/shell-diffusion-in-a-tank-222
Since the governing PDE is just the Laplacian of the field variable (V), or precisely, div(- C*grad(V)) = 0 where C = sigma*d , one would expect that the solution to the PDE, being the Voltage, should satisfy the PDE everywhere.
Now I tried plotting the PDE, along a line in the z-direction, in the following form and I expected to get zero everywhere:
dtang(sigma*d*dtang(V,x),x)+dtang(sigma*d*dtang(V,y),y)+dtang(sigma*d*dtang(V,z),z)
or equivalently:
d(sigma*d*VTx,x)+d(sigma*d*VTy,y)+d(sigma*d*VTz,z)
to my surprise, the answer to the mentioned expression is actually very far from zero (to the order of 10^8). of course, refining the mesh won't help either. could anyone please help me with this? is there a problem with my understanding of the tangential derivatives?
Hello Mohammad Miraskari
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