A question about FDM in cylindrical coordinates.
Hello everybody!
My question is about solving equations (for example Laplass or Poisson equations) in cylindrical coordinates using the finite difference method. Actually I dont understand which boundary conditions should I apply for this finitedifference scheme in the point r=0 (or r = "very small dr", one dr step for example). In the point r=R I use (for example) F(r,fi) = 0; In fi=0 and fi= 2pi I use F(r,0) = F(r,2pi); These are the 3 of 4 sides of the corresponding rectangualar. But which boundary condition should i write for the point r=0 (or r=dr) ? May be, F(0,fi) = F(o,fi+pi)? Or F(0,fi) = F(0, any fi)? Please, share your experience. 
Re: A question about FDM in cylindrical coordinate
It depends on how discretize your domain, for example, cellcentered or celledged, etc.

Re: A question about FDM in cylindrical coordinate
Sorry, can you clarify your answer?
I discretize my domain using the standart 5point Laplass operator approximation. Without coefficients it is like that: d2F/dr2 = F(r+1,fi)  2F(r,fi) + F(r1,fi) dF/dr = F(r+1,fi)  F(r1,fi) F = F(r,fi) dF/dfi = F(r,fi+1)  2*F(r,fi) + F(r,fi1) ... and so on. So, we have 5diagonal matrix (except for boundary conditions for fi) with F(r,fi) on the main diagonal. 
Re: A question about FDM in cylindrical coordinate

Re: A question about FDM in cylindrical coordinate
Use dF/dR = 0 at r=0.

Re: A question about FDM in cylindrical coordinate
See paper by Morinishini et al. (2004) in journal of computational physics (and references there). Remember that the centreleine in a nonphysical (grid generated) singularity and special treatment is needed there.

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