Direct_nl.sif

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!!                                       !!
!! Test for Weertman friction law        !!
!! Generate perfect model solution
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!! PARAMETERS
$L = 20.0e3
$Slope = 0.1 * pi / 180.0
!### physical constants
$yearinsec = 365.25*24*60*60
$rhoi = 900.0/(1.0e6*yearinsec^2)   
$gravity = -9.81*yearinsec^2
$n = 3.0
$eta = (2.0*100.0)^(-1.0/n)
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Header
  Mesh DB "." "rectangle"
End
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Simulation
  Coordinate System  = Cartesian 3D
  Simulation Type = Steady        

  ! Internal extrusion
  Extruded Mesh Levels = Integer 5

  Steady State Min Iterations = 1
  Steady State Max Iterations = 1

  Post File = "Direct_nl.vtu"
  OutPut File = "Direct_nl.result"

  max output level = 3
End

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! The ice 
Body 1
  Equation = 1
  Body Force = 1
  Material = 1
  Initial Condition = 1
End

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Initial Condition 1
  Pressure = Real 0.0 
  Velocity 1 = Real 0.0 
  Velocity 2 = Real 0.0 
  Velocity 3 = Real 0.0

  C = Variable Coordinate 1, Coordinate 2
     Real  MATC "5.0e-3*(1.0 + sin(2.0*pi*tx(0)/L)*sin(2.0*pi*tx(1)/L))"
End

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Body Force 1
  Flow BodyForce 1 = Real 0.0
  Flow BodyForce 2 = Real 0.0
  Flow BodyForce 3 = Real $gravity
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Material 1
  Density = Real $rhoi 
  Viscosity Model = String "power law"
  Viscosity = Real $eta                       
  Viscosity Exponent = Real $1.0/n                
  Critical Shear Rate = Real 1.0e-10
End

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Solver 1  
  Equation = "MapCoordinate"
  Procedure = "StructuredMeshMapper" "StructuredMeshMapper"
  Active Coordinate = Integer 3
End

Solver 2
  Equation = "Stokes-Vec"
  Procedure = "IncompressibleNSVec" "IncompressibleNSSolver"

  Div-Curl Discretization = Logical False
  Element = "p:1 b:4"

  Flow Model = Stoke
  Stokes Flow = logical true

  !Relative Integration Order = -1

  !linear settings:
  !------------------------------
  Linear System Solver = Iterative
  Linear System Iterative Method = GCR
  Linear System GCR Restart =  250
  Linear System Max Iterations  = 1000
  Linear System Preconditioning = ILU0
  Linear System Convergence Tolerance = 1.0e-08

  Linear System Residual Output = 100

  !Non-linear iteration settings:
  !------------------------------ 
  Nonlinear System Max Iterations = 50
  Nonlinear System Convergence Tolerance  = 1.0e-6
  Nonlinear System Newton After Iterations = 5
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Reset Newton = Logical True

 !!!!!!!!
  Exported Variable 1 = C
End

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Equation 1
  Active Solvers(2) = 1 2
End
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!!! BC (y=y0)    
Boundary Condition 1
  Target Boundaries = 1
End

!!! BC (x=xmax) 
Boundary Condition 2
  Target Boundaries = 2
  Periodic BC = 4
  Periodic BC Translate(3) =  $L 0.0 0.0
  Periodic BC Velocity 1  = Logical True
  Periodic BC Velocity 2  = Logical True
  Periodic BC Velocity 3  = Logical True
  Periodic BC Pressure = Logical True
End

!!! BC (y=ymax)   
Boundary Condition 3
  Target Boundaries = 3
  Periodic BC = 1
  Periodic BC Translate(3) = 0.0 $L 0.0
  Periodic BC Velocity 1  = Logical True
  Periodic BC Velocity 2  = Logical True
  Periodic BC Velocity 3  = Logical True
  Periodic BC Pressure = Logical True
End

!!! BC  (x=x0) 
Boundary Condition 4
  Target Boundaries = 4
End

!!! bedrock
Boundary Condition 5
  Flow Force BC = Logical True

  Normal-Tangential Velocity = Logical True
  Velocity 1 = Real 0.0e0

  Weertman Friction Coefficient = Equals C
  Weertman Exponent = Real $1.0/3.0
! Cut-off such that argument is not smaller than this
  Friction Linear Velocity = Real 1.0e-4

  Bottom Surface = Variable Coordinate 1
     Real MATC "-tx*tan(Slope)-1000.0"
End

!!! free surface
Boundary Condition 6
  Top Surface = Variable Coordinate 1
     Real MATC "-tx*tan(Slope)"
End

!### REFERENCE SOLUTION
Solver 2 :: Reference Norm = 17.678308
Solver 2 :: Reference Norm Tolerance = Real 1.0e-4