Errors for temperature field occur in a multiphysics problems

[杨荣伟]

Dear all,

We are dealing with a multiphysics problems for porous material, accounting for displacement field, temperature field and pore pressure field. The governing equations are expressed as follows,

 

     We implemented the work based on Step26 (We really appreciated that). Now the problem we encountered is that there still exist unexpected errors on the temperature field in Deal II solution (see the figures (circles) enclosed in attachment ). We suspect that the errors arise from the large magnitude of thermal conductivity (K_T in the equations in the attachment), which is equal to 10^6, which will render the stiffness matrix being errous. Does anyone can help us to figure out the critical errors and make any suggestions? 

                                              BTW, we use solver GMRES, Thanks a lot in advance !

              We are looking forward to hearing from you at your earliest convenience!!

   

[Wolfgang Bangerth]

On 9/5/24 01:07, 杨荣伟 wrote:
>      We implemented the work based on Step26 (We really appreciated
> that). Now the problem we encountered is that there still exist
> unexpected errors on the temperature field in Deal II solution (see
> the figures (circles) enclosed in attachment ). We suspect that the
> errors arise from the large magnitude of thermal conductivity (K_T in
> the equations in the attachment), which is equal to 10^6, which will
> render the stiffness matrix being errous. Does anyone can help us to
> figure out the critical errors and make any suggestions?

At the end of the day, you will have to develop the skills to debug
these sorts of problems -- this will not be the last time you wonder
about the correctness of your program :-)

In your case, I think you are using an adaptive mesh. Make the problem
simpler: Does the solution look correct if you are using a uniformly
refined mesh? If yes, are you using a higher-order element (e.g.,
quadratic shape functions)? If so, go back to linear elements and make
sure the solution is correct. If so, you can try quadratic elements
again, but make sure that what you are visualizing is an adequate
representation of the actual solution -- see

https://github.com/dealii/dealii/wiki/Frequently-Asked-Questions#in-my-graphical-output-the-solution-appears-discontinuous-at-hanging-nodes

There are many more directions one can go into, but these are perhaps
good starting points already.

Best
W.

[sper...@gmail.com]

Thanks，Prof. Bangerth, we have used uniform mesh, and the errors appeared also. We will check and verify the questions you posed. Thanks a lot for your kindly reply! best regards Yours sincerely Rongwei

---- 回复的原邮件 ----

发件人	Wolfgang Bangerth<bang...@colostate.edu>
日期	2024年09月06日 00:19
收件人	dea...@googlegroups.com
抄送至
主题	Re: [deal.II] Errors for temperature field occur in a multiphysics problems

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[Rongwei YANG]

Dear Wolfgang,

Maybe I had not make my question clear. I dont think the question we encountered is not graphical output, instead, I think the the problem we encountered is numerical issue in Deal II.  For example, when we take thermal conductivity as 1e6 (the real value of the problem), there always exhibit erroneous results in the figure (see the figure below), in temperature distribution, as high as 24 degree centigrate in the figure, but as theoretical calculation,  all the temperatures within the figure should range between 0  and -50 degree. On the contrary, when thermal conductivity was taken as 1e2, the simulation results work well. Moreover, when we make the simulation via Matlab, the simulation results work well even thermal conductivity was taken as 1e6. So we suspect that the high magnitude of thermal conductivity in coupled equation significantly affects the simulation results. But we are really not sure where is the problem and how to fix it, any other suggestions?

 We also found in other step (e.g. step 34), temperature-displacement-pressure multi-field problem was implemented by decoupling the temperature field. 

Best regards!

Rongwei

Dr. Rongwei Yang (杨荣伟)

School of Civil Engineering, Tianjin University, 

135 Yaguan Rd, Jinnan District, Tianjin 300350, China P.R.

Email: yan...@tju.edu.cn

http://jgxy.tju.edu.cn/teachers.asp?id=221

sper...@gmail.com <sper...@gmail.com> 于2024年9月6日周五 09:19写道：

[Wolfgang Bangerth]

Rongwei:

> Maybe I had not make my question clear. I dont think the question we
> encountered is not graphical output, instead, I think the the problem we
> encountered is numerical issue in Deal II.  For example, when we take thermal
> conductivity as 1e6 (the real value of the problem), there always
> exhibit erroneous results in the figure (see the figure below), in temperature
> distribution, as high as 24 degree centigrate in the figure, but as
> theoretical calculation,  all the temperatures within the figure should range
> between 0  and -50 degree.

I see. Here are two thoughts:
* Just because something is true for the solution of the exact PDE does not
mean that it is true for the discrete solution. This is most apparent for
hyperbolic conservation laws -- think, the simple advection equation
beta.grad u=f
For these, the exact solution may have discontinuities but not over- or
undershots. But the *discrete* solution has over- and undershots unless you do
something specific about it. The same is true for other equations: Just
because you know that the exact solution should be between -50 and 0 degrees
does not mean that the discrete solution needs to satisfy the same property
(although one would hope that at least in the limit h->0 it should).

* One of the things that happens when you have large jumps in the conductivity
is that you lose coercivity of the bilinear form. A consequence is that the
matrix becomes ill-conditioned. You might want to see whether choosing a
smaller tolerance in the linear solver helps, or perhaps using a direct solver.

> On the contrary, when thermal conductivity was
> taken as 1e2, the simulation results work well. Moreover, when we make the
> simulation via Matlab, the simulation results work well even thermal
> conductivity was taken as 1e6. So we suspect that the high magnitude of
> thermal conductivity in coupled equation significantly affects the simulation
> results. But we are really not sure where is the problem and how to fix it,
> any other suggestions?

If you find that it works with Matlab, then you might want to compare the
matrix and right hand side you get from both implementations, on a very coarse
mesh. If they are different, you should find out why they are.

Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Rongwei YANG]

Thanks for the kindly suggestions.

Best regards!!

Dr. Rongwei Yang (杨荣伟)

School of Civil Engineering, Tianjin University, 

135 Yaguan Rd, Jinnan District, Tianjin 300350, China P.R.

Email: yan...@tju.edu.cn

http://jgxy.tju.edu.cn/teachers.asp?id=221

Wolfgang Bangerth <bang...@colostate.edu> 于2024年9月10日周二 23:41写道：

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[Luca Heltai]

Dear Rongwei,

A few points come to mind:

- what solver are you using?

- if it is iterative, what is the tolerance you are setting for your solver?

- does the picture change if you decrease the solver tolerance?

A contrast of 1e6 in the coefficients leads to a matrix that is more ill-conditioned (precisely: a factor 1e4 worse w.r.t. contrast=1e2). A small perturbation (in the order of eps=1e-15) will result in a difference in the result that is a factor 1e4 larger w.r.t. before. 

Have you considered all these things in choosing a preconditioner, a solver, and the various tolerances?

Luca

Il giorno 13 set 2024, alle ore 07:18, Rongwei YANG <sper...@gmail.com> ha scritto:



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