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

[Ying He]

On 2016-07-11 10:48, 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 (Ying He) (Ying He)
> 
> 
> ----------------------------------------------------------------------
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> Message: 1
> Date: Mon, 11 Jul 2016 10:48:24 -0700
> From: Ying He <yinghe at math.ucdavis.edu>
> To: 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 (Ying He)
> Message-ID: <0184fa181ad1337f23fbd4da23e7f556 at math.ucdavis.edu>
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> On 2016-07-10 12:00, aspect-devel-request at geodynamics.org wrote:
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>> Today's Topics:
>> 
>>    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
> 
I just realized that the correctly formula should be

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

therefore we imposed

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

and we only assume k and \nu positive numbers, so it could be the 
magnitude of (k +\nu) affecting the final flux calculation. I'll check 
the value dT/dn instead.


> 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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> 
> --
> Best,
> Ying
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-- 
Best,
Ying He