I have created two basic hand solvable test geometry's, a wire loop and parallel wire to test my understanding of the solver. With each geometry I only see approximately 42% of the expected inductance which stems from an incorrect total flux. The simulated current density (and by extension total current used in the above formula) always matches hand calculations. I have tried stimulating through boundary and body force cases. I am post processing through paraview and calculating flux with the surface flow filter (Integrate filter gives same answer) through an extracted surface. I have also visually inspected the flux field orientation of the entire simulation and extracted surface areas to make sure they are as expected.

Am I defining my Dirichlet conditions incorrectly?

Am I deriving the total flux density incorrectly in paraview?

Am I over/under constraining something?

The attached images show:

-Parallel wire geometry

-Parallel wire extracted plane an integration area for flux

-Parallel wire flux field

-Loop geometry

Sif for parallel wire boundary stimulation

Code: Select all

```
Check Keywords "Warn"
Header
Mesh DB "."
End
Simulation
Max Output Level = 5
Coordinate System = "Cartesian"
Simulation Type = Steady
Steady State Max Iterations = 1
Output Intervals(1) = 1
!Coordinate Scaling = 1.0e-3
End
Constants
Gravity(4) = 0 0 -1 9.81 ! N | m s^-2
Stefan Boltzmann = 5.67e-08 ! W m^-2 °K^-4 | kg s^-3 °K^-4
Permittivity of Vacuum = 8.8542e-12 ! F m^-1 | A^2 s^4 kg^-1 m^-3
Permeability of Vacuum = 1.2566e-6 ! H m^-1 | kg m s^-2 A^-2
Boltzmann Constant = 1.3807e-23 ! J °K^-1 | m^2 kg s^-2 °K^-1
Unit Charge = 1.602e-19 ! C | A s
End
Body 1
Name = "Wire1"
Equation = 1
Material = 1
End
Body 2
Name = "Air"
Equation = 1
Material = 2
End
Body 3
Name = "Wire2"
Equation = 1
Material = 1
End
Material 1
Name = "Cu"
Relative Permittivity = 1
Relative Permeability = 1
Electric Conductivity = 58e6
End
Material 2
Name = "Air"
Relative Permittivity = 1.0
Relative Permeability = 1.0
Electric Conductivity = 0.0
End
Equation 1
Active Solvers(2) = 1 2
End
Solver 1
Equation = "MGDynamics"
Variable = "AV"
Procedure = "MagnetoDynamics" "WhitneyAVSolver"
Element = n:1 e:1
Fix Input Current density = Logical True
Automated Source Projection BCs = Logical False
Linear System Symmetric = True
Linear System Solver = "Iterative"
Linear System Preconditioning = none
Linear System Residual Output = 50
Linear System Max Iterations = 1000
Linear System Iterative Method = GCR
Linear System Convergence Tolerance = 1.0e-5
BicgStabl Polynomial Degree = 4
Linear System Abort Not Converged = False
End
Solver 2
Equation = "MGDynamicsCalc"
Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
Linear System Symmetric = True
Potential Variable = String "AV"
Calculate Current Density = Logical True
Calculate Electric Field = Logical True
Calculate Magnetic Field Strength = Logical True
Calculate Joule Heating = True
Steady State Convergence Tolerance = 0
Linear System Solver = "Iterative"
Linear System Preconditioning = None
Linear System Residual Output = 0
Linear System Max Iterations = 2000
Linear System Iterative Method = CG
Linear System Convergence Tolerance = 1.0e-8
Calculate Nodal Fields = Logical False
Impose Body Force Potential = Logical True
Impose Body Force Current = Logical True
Discontinuous Bodies = True
End
Solver 3
Exec Solver = after all
Equation = "ResultOutput"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = inductor
Vtu format = Logical True
Discontinuous Bodies = Logical True
End
Boundary Condition 1
Name = "WireStart"
Target Boundaries(1) = 1
!Coil Start = Logical True
!AV {e} 1 = Real 0.0
!AV {e} 2 = Real 0.0
!AV {e} 3 = Real 0.0
!AV = Real 10e-3
Electric Current Density = Real 3.18e3
End
Boundary Condition 2
Name = "WireEnd"
Target Boundaries(3) = 2 6 7
!Coil End = Logical True
AV {e} = Real 0.0
!Electric Current Density = Real 125e3
AV = Real 0
End
Boundary Condition 3
Name = "Torus_surface"
Target Boundaries(1) = 4 !Surface 3&5 are wire boundaries
AV {e} = Real 0.0
End
```

Code: Select all

```
Check Keywords "Warn"
Header
Mesh DB "."
End
Simulation
Max Output Level = 5
Coordinate System = "Cartesian"
Simulation Type = Steady
Steady State Max Iterations = 1
Output Intervals(1) = 1
!Coordinate Scaling = 1.0e-3
End
Constants
Gravity(4) = 0 0 -1 9.81 ! N | m s^-2
Stefan Boltzmann = 5.67e-08 ! W m^-2 °K^-4 | kg s^-3 °K^-4
Permittivity of Vacuum = 8.8542e-12 ! F m^-1 | A^2 s^4 kg^-1 m^-3
Permeability of Vacuum = 1.2566e-6 ! H m^-1 | kg m s^-2 A^-2
Boltzmann Constant = 1.3807e-23 ! J °K^-1 | m^2 kg s^-2 °K^-1
Unit Charge = 1.602e-19 ! C | A s
End
Body 1
Name = "Wire1"
Equation = 1
Material = 1
Body Force = 1
End
Body 2
Name = "Air"
Equation = 1
Material = 2
End
Body 3
Name = "Wire2"
Equation = 1
Material = 1
End
Material 1
Name = "Cu"
Relative Permittivity = 1
Relative Permeability = 1
Electric Conductivity = 58e6
End
Material 2
Name = "Air"
Relative Permittivity = 1.0
Relative Permeability = 1.0
Electric Conductivity = 0.0
End
Equation 1
Active Solvers(2) = 1 2
End
Solver 1
Equation = "MGDynamics"
Variable = "AV"
Procedure = "MagnetoDynamics" "WhitneyAVSolver"
Element = n:1 e:1
Fix Input Current density = Logical True
Automated Source Projection BCs = Logical False
Linear System Symmetric = True
Linear System Solver = "Iterative"
Linear System Preconditioning = none
Linear System Residual Output = 50
Linear System Max Iterations = 1000
Linear System Iterative Method = GCR
Linear System Convergence Tolerance = 1.0e-5
BicgStabl Polynomial Degree = 4
Linear System Abort Not Converged = False
End
Solver 2
Equation = "MGDynamicsCalc"
Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
Linear System Symmetric = True
Potential Variable = String "AV"
Calculate Current Density = Logical True
Calculate Electric Field = Logical True
Calculate Magnetic Field Strength = Logical True
Calculate Joule Heating = True
Steady State Convergence Tolerance = 0
Linear System Solver = "Iterative"
Linear System Preconditioning = None
Linear System Residual Output = 0
Linear System Max Iterations = 2000
Linear System Iterative Method = CG
Linear System Convergence Tolerance = 1.0e-8
Calculate Nodal Fields = Logical False
Impose Body Force Potential = Logical True
Impose Body Force Current = Logical True
Discontinuous Bodies = True
End
Solver 3
Exec Solver = after all
Equation = "ResultOutput"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = inductor
Vtu format = Logical True
Discontinuous Bodies = Logical True
End
Body Force 1
Name = "Current"
Current Density 3 = real 150e3
End
Boundary Condition 1
Name = "Farfield"
Target Boundaries(1) = 3 4 5 !Surface 3&5 are wire boundaries
AV {e} = Real 0.0
End
```

Mike