[aspect-devel] Free-Surface in 3d

[Ian Rose]

Any updates on this, Avery?

With regards to the stabilization and scaling thereof:  The units are the
correct, though the parameters for the stabilization term normally live on
the RHS of the system (namely gravity and density).

One way of looking at this is from the perspective of
nondimensionalization, as Wolfgang said.  The introduction of the free
surface essentially adds a new nondimensional number to the system. There
is a couple of equivalent choices you could make, but one that works is
thinking about the ratio of internal density anomalies (relevant to
convection) to the reference density (which is relevant to relaxation of
the surface).

So the reason convection-box was having difficulties (as far as I can tell)
is that it was assuming that there is only one nondimensional number in the
system (the Rayleigh number), so you can increase gravity with impunity as
long as you decrease some other parameter correspondingly (in this case
thermal expansivity).  When you introduce the free surface, however, there
is an additional nondimensional number, so you need to be a bit more
careful about rescaling various parameters.

As for what to do about this, I am not sure what to say, other than to be
somewhat careful about the system parameters.

Best,
Ian


On Sun, Jul 26, 2015 at 5:09 PM, Wolfgang Bangerth <bangerth at tamu.edu>
wrote:

> On 07/22/2015 12:34 PM, Ian Rose wrote:
>
>>
>> If we consider the typical size of entries in the normal system matrix,
>> we get
>> something like \eta L, where \eta is the viscosity and L is a lengthscale
>> for
>> the cells.  For free surface problems, the surface should be stabilized.
>> The
>> stabilization term is typically of order \rho g \Delta t L^2.  The ratio
>> of
>> the size of the stabilization term to the normal matrix elements is then
>> \rho
>> g L \Delta t / \eta. For most problems of geophysical relevance this term
>> will
>> be on the small (but not negligible, since we need it for stabilization!)
>> side, something like 10^{-1} - 10^{-2},
>>
>> However, the convection-box-3d parameter file has some odd values which
>> change
>> the story.  In particular, the value for gravity is large (10^{16}!!) and
>> the
>> value for viscosity is small (1).  So the stabilization term absolutely
>> dominates the matrix entries by around nine or ten orders of magnitude.
>> You
>> can imagine that that would be bad.  I would note that the unusual values
>> for
>> the convection-box parameter files have caused problems in the past, see,
>> for
>> example issue #94.  Perhaps Wolfgang or Timo would have some further
>> insight here.
>>
>
> I haven't followed the development of the free surface terms from a
> mathematical perspective (I only looked at code issues), so I have nothing
> of real substance to offer other than the following question:
>
> Stabilization terms are usually added to existing terms in the equation.
> As usual, the terms you add need to have the same physical units as the
> existing terms. Is this not the case here? Or is it the case that you have
> a stabilization parameter that has physical dimensions? One usually avoids
> such scaling problems by defining the stabilization term as the product of
> - a dimensionless number
> - a product of physical constants (such as the viscosity, density, etc) so
>   that the overall term has the correct units consistent with the other
>   terms in the equation
> - the stabilization itself (e.g., the Laplacian of some quantity)
>
> This way, one only has to tune the dimensionless first factor, and the
> whole thing will continue to work in other settings.
>
> Best
>  Wolfgang
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                 www: http://www.math.tamu.edu/~bangerth/
>
>
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