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

Sif for parallel wire body force 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

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

Thanks everyone,

Mike