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Current conservation issue when integrating charge density
Posted 04.04.2016, 13:30 GMT-4 Low-Frequency Electromagnetics, Modeling Tools & Definitions, Parameters, Variables, & Functions, Results & Visualization, Studies & Solvers Version 5.1, Version 5.2 1 Reply
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I am working with an AC/DC, 3D, Stationary, Electric Currents model.
I am currently studying charge density between deep brain stimulation electrodes of different surface areas and geometries. To represent an oversimplified electrode, we created a cylinder with high conductivity (1e10 S/m) and a point current source at it's center. The cylinder was in a conductive medium similar to the brain, 0.2 S/m.
When evaluating this simplified problem, I encountered some error that seems violate current conservation. Specifically, I am finding 47% error between the point current source (0.001 A) and the integral of current density (ec.normJ) over the surface area of the cylinder.
Note: I did conduct a mesh convergence study - below the current mesh size (0.00002), the error does not notably improve.
I then explored this issue with different geometries (spheres, ellipsoids, cubes, rectangular boxes, etc). See page 1 of the attached TroubleshootingComsol.pdf for the results. To quickly summarize, symmetric geometries - spheres and cubes - integrate to a current within 2% error. However, non symmetric geometries, ellipsoids, cylinders, rectangular boxes - have unacceptable integration error (11-63%).
*****Question: Any ideas of the possible sources of error in the simple problem? Any suggestions to further troubleshoot?
An an alternative method, I also explored representing the electrode as a cylindrical shell with floating potential of 0.001 A. In this case, the integral of normJ is 0.0004- less than half than expected. The integral of nJ was closer - 0.0009. To troubleshoot this, I went back to a sphere, with similar results - integral of normJ was 0.00048 and integral of nJ was 0.00097. See page 2 of the TroubleshootingComsol.pdf for more details.
*****Question: I originally believed that normJ, the total current density norm, was the output of interest when studying charge density on a surface, but I am confused by the fact that it is substantially lower than nJ in the floating potential situation.
I greatly appreciate in advance any tips, explanations or corrections.
Sincerely,
Ashley
I am currently studying charge density between deep brain stimulation electrodes of different surface areas and geometries. To represent an oversimplified electrode, we created a cylinder with high conductivity (1e10 S/m) and a point current source at it's center. The cylinder was in a conductive medium similar to the brain, 0.2 S/m.
When evaluating this simplified problem, I encountered some error that seems violate current conservation. Specifically, I am finding 47% error between the point current source (0.001 A) and the integral of current density (ec.normJ) over the surface area of the cylinder.
Note: I did conduct a mesh convergence study - below the current mesh size (0.00002), the error does not notably improve.
I then explored this issue with different geometries (spheres, ellipsoids, cubes, rectangular boxes, etc). See page 1 of the attached TroubleshootingComsol.pdf for the results. To quickly summarize, symmetric geometries - spheres and cubes - integrate to a current within 2% error. However, non symmetric geometries, ellipsoids, cylinders, rectangular boxes - have unacceptable integration error (11-63%).
*****Question: Any ideas of the possible sources of error in the simple problem? Any suggestions to further troubleshoot?
An an alternative method, I also explored representing the electrode as a cylindrical shell with floating potential of 0.001 A. In this case, the integral of normJ is 0.0004- less than half than expected. The integral of nJ was closer - 0.0009. To troubleshoot this, I went back to a sphere, with similar results - integral of normJ was 0.00048 and integral of nJ was 0.00097. See page 2 of the TroubleshootingComsol.pdf for more details.
*****Question: I originally believed that normJ, the total current density norm, was the output of interest when studying charge density on a surface, but I am confused by the fact that it is substantially lower than nJ in the floating potential situation.
I greatly appreciate in advance any tips, explanations or corrections.
Sincerely,
Ashley
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1 Reply Last Post 24.04.2016, 06:35 GMT-4
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Posted:
9 years ago
In order to calculate flux accurately, you need to use weak constraints. You can turn it on by first selecting the advanced physics settings then in the boundary condition settings, you should see a check box for using weak constraints.