Green's Functions for Diffusion

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Contributed by: Brian Vick (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The solution for the Green's function on a finite domain with general boundary conditions is constructed from solutions for an infinite domain using the method of images. In order to see the influence of boundary conditions, place the source point near a boundary and adjust the boundary parameter, .

Snapshot 1: the source point is inside the region, far away from boundaries

Snapshot 2: the source point is near an insulated boundary ()

Snapshot 3: the source point is near a zero potential boundary ( large)

Nomenclature:

= Green's function (1/)

= position (m)

= time (s)

= source location (m)

= source time (s)

= diffusivity (/s)

, = boundary coefficients (1/m)



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