I have included the code below for your analysis. Could you please help us understand the reason behind this deviation?

Furthermore, I kindly request your assistance in reviewing the attached Google Drive link. https://drive.google.com/file/d/1z26iNv ... sp=sharing

It contains all the necessary files for the calculation. If you could take a look and provide guidance based on those files, I would greatly appreciate it.

mag.sif

Code: Select all

```
INCLUDE mesh/mesh.names
Header
Mesh DB "mesh"
Results Directory "magnetic_results"
End
include mag_params.dat
Simulation
Max Output Level = 3
Coordinate System = Cartesian 3D
!Coordinate Scaling = 0.001
Simulation Type = Transient
Timestepping Method = BDF
BDF Order = 2
Output Intervals(1) = 1
Timestep Sizes = $ 1/f/50
Timestep Intervals = 150
Use Mesh Names = Logical True
End
! Air
Material 1
Relative Permeability = 1
Electric Conductivity = 0
End
! Copper
Material 2
Relative Permeability = 1
Electric Conductivity = 1e3
End
Body 1
Name = Air
Equation = 1
Material = 1
Target Bodies = 1
End
Body 2
Name = U_1
Equation = 2
Material = 2
Target Bodies = 2
Body Force = 1
Initial Condition = 1
Alpha reference (3) = Real 0 1 0
Beta reference (3) = Real 0 0 1
End
Equation 1
Active Solvers(6) = 5 6 7 8 9 10
End
Equation 2
Active Solvers(10) = 1 2 3 4 5 6 7 8 9 10
End
Solver 1
Exec Solver = Before all
Procedure = "DirectionSolver" "DirectionSolver"
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Max Iterations = 5000
Linear System Convergence Tolerance = 1.0e-10
Linear System Abort Not Converged = True
Linear System Residual Output = 1000
Equation = Direction Alpha
Variable = Alpha
End
Solver 2
Exec Solver = Before all
Procedure = "DirectionSolver" "DirectionSolver"
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Max Iterations = 5000
Linear System Convergence Tolerance = 1.0e-10
Linear System Abort Not Converged = True
Linear System Residual Output = 1000
Equation = Direction Beta
Variable = Beta
End
Solver 3
Exec Solver = Before All
Equation = Transformation matrix
Procedure = "CoordinateTransform" "RotMSolver"
Variable = -nooutput Dummy
Optimize Bandwidth = False
Polar Decomposition Determinant Tolerance = Real 1.0e-9
Polar Decomposition Max Iterations = Integer 100
Exported Variable 1 = -nooutput RotM E[RotM E:9]
Exported Variable 2 = -nooutput Alpha Vector E[Alpha Vector E:3]
Exported Variable 3 = -nooutput Beta Vector E[Beta Vector E:3]
Exported Variable 4 = -nooutput Gamma Vector E[Gamma Vector E:3]
Discontinuous Galerkin = True
End
Solver 4
Exec Solver = Before All
Procedure = "WPotentialSolver" "Wsolve"
Equation = "Wire direction"
Variable = W
Linear System Solver = Iterative
Linear System Iterative Method = CG
Linear System Max Iterations = 10000
Linear System Convergence Tolerance = 1.0e-10
Linear System Abort Not Converged = True
Linear System Residual Output = 1000
End
Solver 5
Exec Solver = Always
Equation = Circuits
Variable = X
Procedure = "CircuitsAndDynamics" "CircuitsAndDynamics"
No Matrix = Logical True
End
Solver 6
Exec Solver = Always
Equation = Magmod3D
Variable = A
Procedure = "MagnetoDynamics" "WhitneyAVSolver"
Stabilize = True
Newton-Raphson Iteration = Logical True
Nonlinear System Max Iterations = 20
Nonlinear System Convergence Tolerance = 1e-6
Export Lagrange Multiplier = Logical True
Linear System Solver = Iterative
Linear System Iterative Method = BicgstabL
Linear System preconditioning = Circuit
Linear System Convergence Tolerance = 1e-7
Linear System Max Iterations = 5000
Linear System Residual Output = 1000
Linear System ILUT Tolerance = 1e-5
BicgstabL polynomial degree = 6
Linear System Abort Not Converged = False
End
Solver 7
Exec Solver = Always
Equation = CalcFields
Potential Variable = A
Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
Linear System Symmetric = True
Steady State Convergence Tolerance = 0
Linear System Solver = "Iterative"
Linear System Preconditioning = None
Linear System Residual Output = 1000
Linear System Max Iterations = 5000
Linear System Iterative Method = CG
Steady State Convergence Tolerance = 1e-6
Linear System Convergence Tolerance = 1.0e-8
Calculate Current Density = Logical True
Calculate Electric Field = Logical True
Calculate Magnetic Field Strength = Logical True
Calculate JxB= Logical True
Calculate Joule Heating = Logical True
End
Solver 8
Exec Solver = after saving
Equation = "ResultOutput"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = magnetic
Output Directory = ./results
Binary Output = Logical True
Vtu format = Logical True
Single Precision = Logical True
!Vector Field 1 = "magnetic flux density e"
!Vector Field 2 = "electric field e"
!Scalar Field 1 = "Joule Heating E"
Discontinuous Bodies = Logical True
End
Solver 9
Exec Solver = Always
Equation = CircOutput
Procedure = "CircuitsAndDynamics" "CircuitsOutput"
End
Solver 10
Exec Solver = After timestep
Equation = scalars1
Procedure = "SaveData" "SaveScalars"
Filename = magnetic_results.dat
Output Directory = magnetic_results
Parallel Reduce = Logical True
End
Boundary Condition 1
Name = BCn Flux Parallel
Target Boundaries(2) = 1 2
A {e} = Real 0
A = Real 0
End
Boundary Condition 2
Name = Alpha0
Target Boundaries = 6
Body 2: Alpha = Real 0
End
Boundary Condition 3
Name = Alpha1
Target Boundaries = 9
Body 2: Alpha = Real 1
End
Boundary Condition 4
Name = Beta0
Target Boundaries = 7
Body 2: Beta = Real 0
End
Boundary Condition 5
Name = Beta1
Target Boundaries = 8
Body 2: Beta = Real 1
End
Boundary Condition 6
Name = coil_begin1
Target Boundaries = 11
A {e} = Real 0
A = Real 0
W = Real 0
End
Boundary Condition 7
Name = coil_end1
Target Boundaries = 5
A {e} = Real 0
A = Real 0
W = Real 1.0
End
```

Code: Select all

```
$ f = 50 ! [Hz] electrical frequency
$ U = 1.0 ! [V] rated voltage
!----------------------------------------------------------
! Stator voltage driven circuits for 3 phases
!----------------------------------------------------------
$ Circuits = 1
!----------------------------------------------------------
! Phase U_plus
!----------------------------------------------------------
! init matrices phase U
! init matrices of Ax' + Bx = Source
$ C.1.variables = 5
$ C.1.perm = zeros(C.1.variables)
$ C.1.A = zeros(C.1.variables,C.1.variables)
$ C.1.B = zeros(C.1.variables,C.1.variables)
! define circuit variables
$ C.1.name.1 = "i_V1"
$ C.1.name.2 = "i_component(1)"
$ C.1.name.3 = "v_V1"
$ C.1.name.4 = "v_component(1)"
$ C.1.name.5 = "u_2_circuit_1"
! -----------------------------------------------------------------------------
! Source Vector Definition
! -----------------------------------------------------------------------------
$ C.1.source.5 = "V1_Source"
! -----------------------------------------------------------------------------
! KCL Equations
! -----------------------------------------------------------------------------
$ C.1.B(0,0) = 1
$ C.1.B(0,1) = 1
! -----------------------------------------------------------------------------
! KVL Equations
! -----------------------------------------------------------------------------
$ C.1.B(1,2) = 1
$ C.1.B(1,4) = 1
$ C.1.B(2,3) = -1
$ C.1.B(2,4) = 1
! -----------------------------------------------------------------------------
! Component Equations
! -----------------------------------------------------------------------------
$ C.1.B(4,2) = 1
Component 1
Name = String Uplus
Body = Integer 2
Coil type = string stranded
Number of Turns = real 10
Electrode Boundaries(2) = Integer 6 5
Circuit Equation Voltage Factor = Real $1/6
End
Body Force 1
Name = "Circuit"
V1_Source = Variable time
Real MATC "sqrt(2/3)*U*sin(tx(0)*2*pi*f)"
End
```