[aspect-devel] questions regarding accuracy of no-heat flux boundary condition and help needed for the right entropy viscosity parameters (Ying He)

[Ying He]

On 2016-07-10 12:00, aspect-devel-request at geodynamics.org wrote:
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>    1. Re: questions regarding accuracy of no-heat flux boundary
>       condition and help needed for the right entropy viscosity
>       parameters (Timo Heister)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Sun, 10 Jul 2016 14:06:13 +0100
> From: Timo Heister <heister at clemson.edu>
> To: aspect-devel <aspect-devel at geodynamics.org>
> Subject: Re: [aspect-devel] questions regarding accuracy of no-heat
> 	flux boundary condition and help needed for the right entropy
> 	viscosity parameters
> Message-ID:
> 	<CAMRj59FcvmSyvXh2q5jFgxeEj5HUwwXrciTg+18xTuN78s94tg at mail.gmail.com>
> Content-Type: text/plain; charset=UTF-8
> 
> Hey Ying,
> 
> I don't have answer to all of your questions, sorry. But:
> 
>> The no heat flux boundary conditions are assigned at left and right 
>> walls of
>> a rectangular box. My first question is that the no heat flux boundary
>> condition seems not preserved for both FEM and DG methods after long 
>> time
>> computation, see attached pdf "T_no_hear_flux_plot.pdf".
> 
> What is the size of the heat flux through the left/right and how does
> it compare to the top/bottom heat flux? If this is non-zero but
> several orders of magnitude smaller, then that is as good as it can
> get. If not, then I don't know.
Hi Timo, thanks for you response. Yes, the left and right flux (O(1)) 
are comparable small to the top and bottom (O(10^4)). However, I still 
think if we assigned the zero non-flux boundary, then it as least should 
be in some lower order accuracy near zero, say (10^{-1})... But perhaps 
you are right, considering the error from the matrix iteration solver.

Also I am more concerned about the right formula to compute the heat 
flux in the  statistics postprocessor. Numerically, we are solving 
transport equation

\rho dT/dt - \grad\cdot (k \grad T) + \grad\cdot (\nu \grad T) + v\cdot 
\grad T = f

where \grad\cdot (\nu \grad T) comes from the artificial entropy 
viscosity. Therefore, in the weak formulation, we assume

  (-k+\nu) dT/dn = 0

which is the no-heat flux condition. However, in the statistics 
postprocessor, we only compute  (-k) dT/dn, so perhaps this is the 
reason why we couldn't have a zero heat flux?

If you look at the attached file velocity.pdf, the non-heat flux becomes 
relatively larger from almost the same time when the velocity becomes 
larger (year 2E+9), where I also assume the artificial entropy viscosity 
becomes larger.


> 
>> As shown in the figure 'timeE10.png', the final solutions of 
>> FEM(right) and
>> DG(left) are very different.
> 
> It looks like a problem with a bifurcation, so there could be more
> than one valid solution. But I agree that they should probably look
> more similar than they currently do.
> 
>> Since the test example
>> uses constant viscosity, the harmonic average will not help here.
> 
> Are you sure? The composition influences the density, which is also
> averaged if you turn it on.
> 
> Interesting example.
> 
> Best,
> Timo
> 
> 
> --
> Timo Heister
> http://www.math.clemson.edu/~heister/
> 
> 
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> End of Aspect-devel Digest, Vol 56, Issue 2
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-- 
Best,
Ying
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