Pathology of discrete diffusion

[Jan Kreft]

Hi swarmers,

some time ago there was a discussion of pathological cases of diffusion
among the list. One such case was brought to light by David Sumpter:

> Hello everyone,
>
> 1. I am using a technique similar to Diffuse 2d for the diffusion of
> heat and am slightly confused by one aspect. Consider a portion of
> lattice with temperatures and first order diffusion:
>
>   0
>  080
>   0 
>
> If the diffusion constant is 1.0 and evaporation rate is 1.0 then the
> centre value will update to 0 while the outside values will update to 
> 2. i.e.
>
>   2
>  202
>   2
>
> This appears somewhat unnatural for heat equations. If the value 8 came
> from some source, you would not expect the source to be colder than
> the surroundings on the next time step........
>
> Am I right about this? Is there a theoretical explanation?
>
> 2. Has anyone got a reference they can give me discussing heat
> diffusion in terms of lattices? I'd be very grateful.
>
> Thanks,
>
> David.
>

I wonder if someone knows of other pathological cases and if there is a
way to avoid such cases within a discrete diffusion frame. Has the above
problem been solved or ignored? 

Any comments welcome.

Cheers,

Jan.



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