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3D Poisson equation problem coupled with Nernst-Planck equation

I used coupled Electrostatics physics and Transport of Diluted Species physics to simulate this problem.
The source term in Poisson equation is the difference between cations and anions.
Usually, the difference should be zero due to the electroneutrality. In some conditions, it would be not.

My problem is that, when I used 2D model, the simulation converged even with a coarse mesh. When it comes to 3D situation, it no longer converged, no matter how fine the mesh is.(as far as I think, the mesh is fine enough)

The error is as below:

Failed to find consistent initial values.
Segregated group 1

Undefined value found.
Undefined value found in the stiffness matrix..
For mesh-case 1 there are 111061 equations giving NaN/Inf in the matrix rows for the variable mod1.H.
and similarly for the degrees of freedom, NaN/Inf in the matrix columns.
Last time step is not converged.

I'm not clear about the numerical methods. It seems that the solving processes of 2D and 3D are quite different. 3D used segregated groups, which is not shown in 2D process.

I need your help.
Thanks in advance.
Mingjie Jia

5 Replies Last Post May 14, 2013, 11:05 AM EDT
COMSOL Moderator

Hello Mingjie Jia

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Posted: 5 years ago Jan 25, 2013, 10:02 AM EST
Hi!

I have the very same problem.
Even for the most simple geometry and boundary conditions the solver does not converge when
'electrostatics' is coupled to 'transport of diluted species'.

Is there any solver setting that needs ajustment in this case? The standard settings do not work, no matter
how simple the model.

First solving the poisson equation and then using this for the nernst-planck equation works fine.
Using those solutions then for solving the coupled equations does not converge, though.

Any hint would be appreciated.

Sincerely,
Andreas

Hi! I have the very same problem. Even for the most simple geometry and boundary conditions the solver does not converge when 'electrostatics' is coupled to 'transport of diluted species'. Is there any solver setting that needs ajustment in this case? The standard settings do not work, no matter how simple the model. First solving the poisson equation and then using this for the nernst-planck equation works fine. Using those solutions then for solving the coupled equations does not converge, though. Any hint would be appreciated. Sincerely, Andreas

Posted: 5 years ago Jan 25, 2013, 2:44 PM EST
I found the solution myself. :-)

1) I had to run the Poisson equation on its own first.
2) Then, using that solution, I solved the NP equation alone.
3) That solution I used for solving the Poisson equation again,
4) solved the NP equation once more and then finaly
5) I solved the coupled PNP equations using the last solution.

I found the solution myself. :-) 1) I had to run the Poisson equation on its own first. 2) Then, using that solution, I solved the NP equation alone. 3) That solution I used for solving the Poisson equation again, 4) solved the NP equation once more and then finaly 5) I solved the coupled PNP equations using the last solution.

Posted: 5 years ago Jan 25, 2013, 7:39 PM EST
Hi

but cant you mange this by a segregated solver with the physics and dependent variables prdered such that you respect your order of solving ?

--
Good luck
Ivar
Hi but cant you mange this by a segregated solver with the physics and dependent variables prdered such that you respect your order of solving ? -- Good luck Ivar

Posted: 5 years ago Mar 8, 2013, 3:56 PM EST
Actually, I did not solve this problem, I just forgot to couple NP back to Poisson.

As soon as I add a space-charge density F*(c1-c2) to the electrostatics interface the solver does not find a solution.
No matter how simple the geometry is. It works flawlessly for 2D axisymmetric, though.

I don't find any example models on this topic in the database.

Does anybody got Poisson-Nernst-Planck to work in 3D?
Actually, I did not solve this problem, I just forgot to couple NP back to Poisson. As soon as I add a space-charge density F*(c1-c2) to the electrostatics interface the solver does not find a solution. No matter how simple the geometry is. It works flawlessly for 2D axisymmetric, though. I don't find any example models on this topic in the database. Does anybody got Poisson-Nernst-Planck to work in 3D?

Posted: 4 years ago May 14, 2013, 11:05 AM EDT

I used coupled Electrostatics physics and Transport of Diluted Species physics to simulate this problem.
The source term in Poisson equation is the difference between cations and anions.
Usually, the difference should be zero due to the electroneutrality. In some conditions, it would be not.

My problem is that, when I used 2D model, the simulation converged even with a coarse mesh. When it comes to 3D situation, it no longer converged, no matter how fine the mesh is.(as far as I think, the mesh is fine enough)

The error is as below:

Failed to find consistent initial values.
Segregated group 1

Undefined value found.
Undefined value found in the stiffness matrix..
For mesh-case 1 there are 111061 equations giving NaN/Inf in the matrix rows for the variable mod1.H.
and similarly for the degrees of freedom, NaN/Inf in the matrix columns.
Last time step is not converged.

I'm not clear about the numerical methods. It seems that the solving processes of 2D and 3D are quite different. 3D used segregated groups, which is not shown in 2D process.

I need your help.
Thanks in advance.
Mingjie Jia

Dear Sir:
I am a newer of using the Comsol multiphysics and my research is quite similar to you ,I want to quantify the ionic migration and ionic diffusion due to the concentration gradient and electric potential.And I using the NP module as well as the electrostatic module.but I cannot find get the right answer,could you help me to figure out some of the questions?They are listed as below:
1,According to you quote,you use the transport of dilute specie module,does that mean this module is also capable of dealing with Nernst-Planck equation?
2,In Nernst-Planck module,the electroneutrality means there is on liberated ion in the model,it that right?
3,how can I couple the electrostatic with the nernst-planck,because what happens is that the redistribution of the ionic species in the bulk material will influence the electric field,than the electric field will influence the migration of the ion.
I am so sorry to bother,but could you help me with that.I spent 6 weeks on the model and barely made progress.Thank you so much.
[QUOTE] I used coupled Electrostatics physics and Transport of Diluted Species physics to simulate this problem. The source term in Poisson equation is the difference between cations and anions. Usually, the difference should be zero due to the electroneutrality. In some conditions, it would be not. My problem is that, when I used 2D model, the simulation converged even with a coarse mesh. When it comes to 3D situation, it no longer converged, no matter how fine the mesh is.(as far as I think, the mesh is fine enough) The error is as below: Failed to find consistent initial values. Segregated group 1 Undefined value found. Undefined value found in the stiffness matrix.. For mesh-case 1 there are 111061 equations giving NaN/Inf in the matrix rows for the variable mod1.H. and similarly for the degrees of freedom, NaN/Inf in the matrix columns. Last time step is not converged. I'm not clear about the numerical methods. It seems that the solving processes of 2D and 3D are quite different. 3D used segregated groups, which is not shown in 2D process. I need your help. Thanks in advance. Mingjie Jia [/QUOTE] Dear Sir: I am a newer of using the Comsol multiphysics and my research is quite similar to you ,I want to quantify the ionic migration and ionic diffusion due to the concentration gradient and electric potential.And I using the NP module as well as the electrostatic module.but I cannot find get the right answer,could you help me to figure out some of the questions?They are listed as below: 1,According to you quote,you use the transport of dilute specie module,does that mean this module is also capable of dealing with Nernst-Planck equation? 2,In Nernst-Planck module,the electroneutrality means there is on liberated ion in the model,it that right? 3,how can I couple the electrostatic with the nernst-planck,because what happens is that the redistribution of the ionic species in the bulk material will influence the electric field,than the electric field will influence the migration of the ion. I am so sorry to bother,but could you help me with that.I spent 6 weeks on the model and barely made progress.Thank you so much.

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