[CIG-LONG] CIG-LONG Digest, Vol 47, Issue 2

[Guillaume.Duclaux at csiro.au]

Walter,

This confuses me...

What Nicolas did is using a scaling factor of 1e-25 to scale the viscosity of the material from 1e23 Pa.s to 0.01, and then applying the time scaling factor to the diffusivity accordingly.
This is the approach described in Gale's users guide...

Does this mean that in static problems (or at least very slow displacement rates) the viscosity shouldn't be scaled?

Cheers

Gilly




On 19/10/2010, at 3:22 PM, Walter Landry wrote:

> Nicolas RIEL <nicolas.riel at free.fr> wrote:
>> Hi Walter,
>> I attached you a basic input file with temperature diffusivity problems.
>> The model is made of one sphere in middle of a square of 1000m².
>> Diffusivity is set at 1e20, temperature of the sphere is 500K whereas in the
>> square temperature is 300K.
> 
> The short answer is that I think you need to set the viscosity to
> something more realistic.  Right now you have it set at 1e-2, which is
> a bit small for rock.
> 
> The long answer is that there is a mismatch in what the timestep
> should be.
> 
> Gale chooses a time step based on the maximum velocity from the Stokes
> solve and the grid spacing.  In this case, the max velocity is about
> 4.5e7.  You can see where this velocity comes from by doing some
> dimensional analysis
> 
>  Force from temperature perturbation ~ viscosity * v/(length * length)
> 
> =>  alpha * dT * density * gravity ~ viscosity * v/(length * length)
> 
> Putting in some numbers
> 
>  3e-5 * 200 * 2000 * 9.81 ~ 1e-2 * v /(1000 * 1000)
> 
> which implies that v ~ 4e9.  Higher, but in the same ballpark.
> 
> The grid spacing is 1000/100=10.  So that gives a time step
> of about 10/4.5e7 ~ 2e-7.
> 
> However, given a diffusivity of 1e20, that means that, in the time of
> 2e-7, the temperature spreads about sqrt(1e20*2e-7) ~ 4e6.  This is
> much larger than the grid spacing of 10.  This makes the time stepping
> unstable, giving rise to the effects that you see.
> 
> If you increase the viscosity to something more reasonable
> (e.g. 1e20), then the implied velocity would be 22 orders of magnitude
> less.  That, in turn, would reduce the diffusion length scale by 11
> orders of magnitude, making the simulation stable again.
> 
> Cheers,
> Walter Landry
> walter at geodynamics.org
> 
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