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Laplace in spherical coordinates

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Old   December 3, 2007, 14:12
Default Laplace in spherical coordinates
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Harini
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I need to solve a diffusion equation in Spherical coordinates. Can somebody help me with discretisation in each coordinates.

Harini
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Old   December 4, 2007, 10:30
Default Re: Laplace in spherical coordinates
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CycLone
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Why do you need to solve it in spherical coordinates?
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Old   December 6, 2007, 17:35
Default Re: Laplace in spherical coordinates
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Dr_D
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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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