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Diffusion problem with sharp edge
Posted 20 giu 2013, 08:24 GMT-4 Mesh 3 Replies
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Dear all,
Using the 2D general PDE form within COMSOL, I'm trying to solve four coupled differenial equations, in order to obtain the velocity profile of an magnetohydrodynamic flow.
One PDE for the vorticity equation (in the 2D plane)
One PDE for the stream function (in the 2D plane)
One PDE for the velocity of the fluid, perpendicular to the 2D plane
One PDE for the electric potential (in the 2D plane)
These equations are solved for the following geometry:
A container, with a channel cut out of the bottom of the container
As a result this goemetry contains two sharp edges of 270 degrees: at the position where the side walls of the channels are in contact with the bottom of the container.
The walls of the channels have a defined electric potential, and the bottom of the channel, as well as the bottom of the container, have an undefined potential, but must satisfy that the derivative of the potential with respect to the normal must be zero (no electrical current through these walls).
After solving the model, the result of comsol shows an unexpected result around the sharp edges:
The electric current (which can be obtained from the electric potential) at these edges show an exceptional high electric current at the side wall of the channel, close to the edge, and an exceptional low current at the container bottom, close to the edge.
Is there some explanation for this result? To me it looks like a non physical phenomenon. If it is, can someone tell me how to solve this problem?
With kind thanks in advance, Anna
Using the 2D general PDE form within COMSOL, I'm trying to solve four coupled differenial equations, in order to obtain the velocity profile of an magnetohydrodynamic flow.
One PDE for the vorticity equation (in the 2D plane)
One PDE for the stream function (in the 2D plane)
One PDE for the velocity of the fluid, perpendicular to the 2D plane
One PDE for the electric potential (in the 2D plane)
These equations are solved for the following geometry:
A container, with a channel cut out of the bottom of the container
As a result this goemetry contains two sharp edges of 270 degrees: at the position where the side walls of the channels are in contact with the bottom of the container.
The walls of the channels have a defined electric potential, and the bottom of the channel, as well as the bottom of the container, have an undefined potential, but must satisfy that the derivative of the potential with respect to the normal must be zero (no electrical current through these walls).
After solving the model, the result of comsol shows an unexpected result around the sharp edges:
The electric current (which can be obtained from the electric potential) at these edges show an exceptional high electric current at the side wall of the channel, close to the edge, and an exceptional low current at the container bottom, close to the edge.
Is there some explanation for this result? To me it looks like a non physical phenomenon. If it is, can someone tell me how to solve this problem?
With kind thanks in advance, Anna
3 Replies Last Post 26 giu 2013, 07:18 GMT-4
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Posted:
1 decade ago
Dear Anna,
Can you add the Comsol model so that it is easier to see what you have modeled?
Also is it possible to say something about what you do expect, as in what values?
Note that these sharp edges can cause singularities which can be reduced by using fillets. Also reducing the mesh size can help deal with these sharp edges, but will generally increase the higher values near the bend.
Note that if you cannot post the model, some pictures can also help in checking what goes on.
Best regards
Frank
Can you add the Comsol model so that it is easier to see what you have modeled?
Also is it possible to say something about what you do expect, as in what values?
Note that these sharp edges can cause singularities which can be reduced by using fillets. Also reducing the mesh size can help deal with these sharp edges, but will generally increase the higher values near the bend.
Note that if you cannot post the model, some pictures can also help in checking what goes on.
Best regards
Frank
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Posted:
1 decade ago
Dear Frank,
Thank you for your reply.
Unfortunately I cannot attatch the file, but I have added a picture of the electrical current resulting from the potential difference between the two vertical walls. Red is a highly positive current and blue is a strongly negative current.
The two vertical walls have a defined electrical potential, whyle the other walls are electrically insulating.
As you can see the electrical current shows high currents at the sharp edges at which the wall with a defined potential meets an insulating wall.
I expect at these walls a smooth transition in the current. I have no reason the expect the current to rise strongly.
I tried to decrease the size of the mesh strongly, but this did not solve the problem.
You speak of fillets. Where can I define these fillets? (I's using COMSOL 4.3a)
With kind regards,
Anna
Thank you for your reply.
Unfortunately I cannot attatch the file, but I have added a picture of the electrical current resulting from the potential difference between the two vertical walls. Red is a highly positive current and blue is a strongly negative current.
The two vertical walls have a defined electrical potential, whyle the other walls are electrically insulating.
As you can see the electrical current shows high currents at the sharp edges at which the wall with a defined potential meets an insulating wall.
I expect at these walls a smooth transition in the current. I have no reason the expect the current to rise strongly.
I tried to decrease the size of the mesh strongly, but this did not solve the problem.
You speak of fillets. Where can I define these fillets? (I's using COMSOL 4.3a)
With kind regards,
Anna
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Posted:
1 decade ago
Dear Anna,
these are indeed singular points in your model. You set a constraint on the potential which cannot be kept, this will result in very high currents near the corners. As your mesh gets finer, the current gets larger but over a smaller area. The total current will get constant.
I attached an example of what you can do to modify the model so that these singular points are removed. I set the boundary slightly outward from the wall, and inserted fillets to round off the corners (other typical singular points).
Another option is to ignore these singularities. Just use a (much) finer mesh, and you'll notice that the potential distribution is correct. You'll see that several mesh elements away from your singularity the current is as "expected".
If you are interested in the current flowing from your boundary condition, you can enable the weak constraint so that you can evaluate the lagrange multiplier, this gives you more accurate results.
Best regards,
Frank
these are indeed singular points in your model. You set a constraint on the potential which cannot be kept, this will result in very high currents near the corners. As your mesh gets finer, the current gets larger but over a smaller area. The total current will get constant.
I attached an example of what you can do to modify the model so that these singular points are removed. I set the boundary slightly outward from the wall, and inserted fillets to round off the corners (other typical singular points).
Another option is to ignore these singularities. Just use a (much) finer mesh, and you'll notice that the potential distribution is correct. You'll see that several mesh elements away from your singularity the current is as "expected".
If you are interested in the current flowing from your boundary condition, you can enable the weak constraint so that you can evaluate the lagrange multiplier, this gives you more accurate results.
Best regards,
Frank
Attachments: