The implementation of one of the Maxwell's equations in OpenFOAM

liuke870915 · November 16, 2015, 07:04

hello,everybody
My major is megnetohydrodynamics, and I am developing a solver to test the instability of MHD. In the solving process, I need to solve one of the Maxwell's equations,see the first attachment,for a steady electric field, the second term of the right hand of this equation is neglected, and it becomes the second attachment , In OpenFOAM, it should be fvc::curl(B)=mu * J (mu is magnetic permeability, J is the current density, and both of them have known), but, after solving this equation, I got a zero field of B(magnetic field), it means the results of this equation is always zero. I want to know how can I implement this equation on OpenFOAM platform. Anybody can help me. Thank you.

akidess · November 16, 2015, 08:11

You cannot solve for B using fvc, because an element you are trying to compute will be dependent on elements you have not computed yet. A curl is nasty using fvm, because you will have coupling between the vector components. The solution is to change your mathematical model to get rid of the curl.

chriss85 · November 16, 2015, 11:29

You should look if your problem allows to use magnetostatics.
Then you can use the magnetostatic vector potential and, for constant mu, solve laplace(A)=mu * j and then B = curl(A). If you need variable mu things become more difficult. You can look up T-T0-Phi method for one possibility. If you find some better suited method, please let me know

liuke870915 · November 17, 2015, 02:04

dear akidess
thank you, I will have a try. because the cfd-online website can not be used regularly, I respond to your answer with this way! thank you!

liuke870915 · November 17, 2015, 02:09

Dear chriss85
thank you!
This method has been tried, but it is very unstable, so I need find a new way to solve this equation.

chriss85 · November 20, 2015, 06:44

Which method are you talking about? The ones I mentioned are very stable from my experiences.

November 16, 2015, 08:11		#2
akidess Senior Member Anton Kidess Join Date: May 2009 Location: Germany Posts: 1,377 Rep Power: 30	You cannot solve for B using fvc, because an element you are trying to compute will be dependent on elements you have not computed yet. A curl is nasty using fvm, because you will have coupling between the vector components. The solution is to change your mathematical model to get rid of the curl. __________________ On twitter @akidTwit Spend as much time formulating your questions as you expect people to spend on their answer.

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November 16, 2015, 11:29		#3
chriss85 Senior Member Join Date: Oct 2013 Posts: 397 Rep Power: 18	You should look if your problem allows to use magnetostatics. Then you can use the magnetostatic vector potential and, for constant mu, solve laplace(A)=mu * j and then B = curl(A). If you need variable mu things become more difficult. You can look up T-T0-Phi method for one possibility. If you find some better suited method, please let me know

November 17, 2015, 02:04		#4
liuke870915 New Member liuke Join Date: Apr 2013 Posts: 20 Rep Power: 13	dear akidess thank you, I will have a try. because the cfd-online website can not be used regularly, I respond to your answer with this way! thank you!

November 17, 2015, 02:09		#5
liuke870915 New Member liuke Join Date: Apr 2013 Posts: 20 Rep Power: 13	Dear chriss85 thank you! This method has been tried, but it is very unstable, so I need find a new way to solve this equation.

November 20, 2015, 06:44		#6
chriss85 Senior Member Join Date: Oct 2013 Posts: 397 Rep Power: 18	Which method are you talking about? The ones I mentioned are very stable from my experiences.