[aspect-devel] Internal heating in aspect (Ludovic Jeanniot)

[Wolfgang Bangerth]

On 08/29/2018 10:19 AM, Max Rudolph wrote:
> 
>     I think that's the point worth investigating. Since in this case the
>     velocity
>     is zero, one would expect the artificial viscosity to also be at
>     least quite
>     small. Why is it not?
> 
> 
> *Maybe the spherical and 2D annulus geometry models are returning an 
> unhelpful length scale, like planetary radius instead of layer depth?*
> 
> aspect/source/simulator/entropy_viscosity.cc (starting line 191):
> // If the velocity is 0 we have to assume a sensible velocity to calculate
> // an artificial diffusion. We choose similar to nondimensional
> // formulations: v ~ thermal_diffusivity / length_scale, which cancels
>      // the density and specific heat from the entropy formulation. It seems
>      // surprising at first that only the conductivity remains, but remember
>      // that this actually *is* an additional artificial diffusion.
>      if (std::abs(global_u_infty) < 1e-50)
>        return parameters.stabilization_beta *
>               max_conductivity / geometry_model->length_scale() *
>               cell_diameter;

We *divide* by the length scale, so a length scale too large would 
actually make the artificial viscosity too small, not too large.

Regardless, for the spherical shell geometry, the value returned is this:

     template <int dim>
     double
     SphericalShell<dim>::
     length_scale () const
     {
       // as described in the first ASPECT paper, a length scale of
       // 10km = 1e4m works well for the pressure scaling for earth
       // sized spherical shells. use a length scale that
       // yields this value for the R0,R1 corresponding to earth
       // but otherwise scales like (R1-R0)
       return 1e4 * maximal_depth() / (6336000.-3481000.);
     }

(I found this difficult to read, see also 
https://github.com/geodynamics/aspect/pull/2641)

So, assuming you're using an Earth-sized sphere in your examples, the 
length scale returned is 10km, which is far smaller than it needs to be 
if you have no convection in your model. But the geometry model can't 
know this.

I continue to be surprised that the artificial viscosity is so large 
*despite the fact that you have no velocity*. It should scale with the 
velocity, but doesn't seem to (?).

Cheers
  W.



-- 
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Wolfgang Bangerth          email:                 bangerth at colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/