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 Harini December 3, 2007 14:12

Laplace in spherical coordinates

I need to solve a diffusion equation in Spherical coordinates. Can somebody help me with discretisation in each coordinates.

Harini

 CycLone December 4, 2007 10:30

Re: Laplace in spherical coordinates

Why do you need to solve it in spherical coordinates?

 Dr_D December 6, 2007 17:35

Re: Laplace in spherical coordinates

Express the (1/r^2) (r^2 f'(r))' term as follows:

(prime stands for a derivative with respect to r) :

(1/r^2) (r^2 f'(r))' =3\frac{d}{d r^3}(r^2 f'(r))

Note that this means you are taking a first derivative wrt r^3 and not a third derivative. This is what you need to discretize.

Also you can stagger the origin, i.e., take your spatial grid points at (N-.5) dr where N=0,1,2...etc

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