Magnetization Field and inconsistent solution

Numerical methods and mathematical models of Elmer
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Magnetization Field and inconsistent solution

Post by tarta »


I am new to Elmer and I am trying to study the resulting magnetic field when putting a conductive ball in an uniform AC magnetic field.
I built the mesh with GMSH, putting the ball in a box (which is itself a sphere of greater radius), then I tried to use WhitneyHarmonicSolver of Elmer to compute the total magnetic field (which is theoretically known by analytic formulas).

Because I intend to use more complex incident magnetic fields in the future, I tried to use the "Magnetization" field of "Body Force" to define the incident field. The used fortran file just returns a constant value along a direction.

The result is quite correct when the incident field is directed by [0,1,1] but totally wrong when the incident field is along [0,0,1] (or other directions) !?
In particular div(B)=0 seems not to be satisfied close to the ball (the field is not deviated, it just seems to stop when reaching the ball, see attached file).
I do not understand how such a behavior can be explained (the mesh seems perfectly homogeneous)...

Is my approach correct (using "Magnetization" to model incident mag field) ? Do you know what could be wrong / what should I check to fix this issue ?

Thank you by advance for your help.


I defined the conductive ball material as:

Code: Select all

! ball
Material 1
  Name = ball
  Relative Permeability = Real 1.0
  Relative Permittivity = Real 1.0
  Electric Conductivity = Real 63000000.0
The incident field is imposed by:

Code: Select all

! uniform_field
Body Force 1
  Name = champ
  Magnetization 1 = Variable "coordinate" 
            Real Procedure "field_constant" "FieldX"
  Magnetization 2 = Variable "coordinate" 
            Real Procedure "field_constant" "FieldY"
  Magnetization 3 = Variable "coordinate" 
            Real Procedure "field_constant" "FieldZ"
And the solver is parametrized with:

Code: Select all

! WhitneySolver
Solver 1
  Equation = WhitneyHarmonicSolver
  Procedure = "MagnetoDynamics" "WhitneyAVHarmonicSolver"
  Variable = String A[A re:1 A im:1]
  Angular Frequency = Real 60000
  Static Conductivity = True
  Fix Input Current Density = False
  Automated Source Projection BCs = True
  Use Lagrange Gauge = True
  Exec Solver = Always
  Stabilize = True
  Optimize Bandwidth = True
  Linear System Solver = Iterative
  Linear System Convergence Tolerance = 1e-10
  Linear System Iterative Method = BiCGstabl
  BiCGstabl polynomial degree = 2
  Linear System Max Iterations = 1500
  Linear System Residual Output = 300
  Linear System Abort Not Converged = True
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Re: Magnetization Field and inconsistent solution

Post by Rick85 »


I'm also interested in this type of simulation. Have you solved your problem? I also wonder if the body force is correct to use for this type of problem?

I notice that your frequency is high (60kHz) and your conductivity is that of a good conductor. If your ball is not very small (less than 1 mm in radius), I think you can use perfectly conductive boundary condition on your sphere (I have not done that in elmer myself. I'm a new user). Otherwise I think you need a very fine mesh on your sphere, smaller than skin depth going inwards radially.
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