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NDSolve Finite Elements in coordinate systems other than cartesian {x,y,z}?

Evgeniy Evtushenko, MSU
Posted 9 years ago
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POSTED BY: Evgeniy Evtushenko
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Sam, Thanks a lot. You solution actually works. I defined the PDE as 

op = \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(Conc[t, r, z]\)\) - 
  Inactive[Div][
   Inactive[Plus][
    Inactive[Times][Diff, Inactive[Grad][Conc[t, r, z], {r, z}]], 
    Inactive[Times][{0, -Sv}, Conc[t, r, z]]], {r, z}] - 
  Times[Diff/r, \!\(
\*SubscriptBox[\(\[PartialD]\), \(r\)]\(Conc[t, r, z]\)\)]

With this trick everything works fine.
POSTED BY: Evgeniy Evtushenko

Well, in general that's bad news, that Finite Elements (or Inactivate) do not support other coordinate systems. Wolfram claims, that Finite Elements is a very general approach to PDEs. On the other hand, many physical models are really complicated in Cartesian coordinates. But they could be largely simplified by changing the coordinate system. My example is exactly this case. It could be reduced to 2D in cylindrical coordinates instead of 3D in {x,y,z}.

Concerning your suggestion, thanks a lot for your help. Right now I'm on vacations, but I'll definitely try it and reply the result.

POSTED BY: Evgeniy Evtushenko
POSTED BY: Sam Carrettie
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