ismip_SSA_2D.sif

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!                                       !!
!! ISMIP-HOM D020 solved in prognostic   !!
!!   using SSA and thickness solvers     !!
!!                                       !!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


$Step = "SSA_2D"
$L = 20.0e3
$Slope = 0.1 * pi / 180.0

$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)

Header
  Mesh DB "." "rectangle"
End

Constants
! No constant Needed
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simulation
  Coordinate System  = Cartesian 2D 
  Simulation Type = Transient     

  Timestepping Method = "bdf"
  BDF Order = 1
  Output Intervals = 1
  Timestep Intervals =  100 
  Timestep Sizes = 1.0 

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

  !Output File = "ismip_step$Step".result"
  Post File = "test_$Step$.vtu"

  max output level = 3
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! The ice 
Body 1
  Equation = 1
  Body Force = 1
  Material = 1
  Initial Condition = 1
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Initial Condition 1
   SSAVelocity 1 = Real 0.0
   SSAVelocity 2 = Real 0.0

! Thickness
  H = Real 1000.0
! free surface elevation
  Zs = Variable Coordinate 1
    Real MATC "-tx*tan(Slope)"
! bedrock elevation
  Zb = Variable Coordinate 1
    Real MATC "-tx*tan(Slope)-1000.0"

End

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

! to update Zs according to H evolution
  Zs = Variable Zb , H
     REAL MATC "tx(0)+tx(1)"
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Material 1

! Material properties
  Viscosity Exponent = Real $1.0/n                
  Critical Shear Rate = Real 1.0e-10

  SSA Mean Viscosity = Real $eta
  SSA Mean Density = Real $rhoi

! slip coeffs
  SSA Friction Law = String "linear"
  SSA Friction Parameter = Variable coordinate 1 , Coordinate 2
     Real  MATC "1.0e-3*(1.0 + sin(2.0*pi* tx(0) / L)*sin(2.0*pi* tx(1) / L))  
End
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solver 1
  Equation = "SSA"
  Variable = -dofs 2 "SSAVelocity"

  Procedure = "ElmerIceSolvers" "SSABasalSolver"

  Linear System Solver = Direct         
  Linear System Direct Method = umfpack

  Nonlinear System Max Iterations = 100
  Nonlinear System Convergence Tolerance  = 1.0e-12
  Nonlinear System Newton After Iterations = 5
  Nonlinear System Newton After Tolerance = 1.0e-05
  Nonlinear System Relaxation Factor = 1.00

End

!! Thickness solver
Solver 2
   Equation = "Thickness"
   Variable = -dofs 1 "H"

   Exported Variable 1 = -dofs 1 "H Residual"

   Exported Variable 2 = -dofs 1 "dHdt"

   Compute dHdT = Logical True

  Procedure = "ElmerIceSolvers" "ThicknessSolver"
   Before Linsolve = "EliminateDirichlet" "EliminateDirichlet"

   Linear System Solver = Iterative
   Linear System Max Iterations = 1500
   Linear System Iterative Method = BiCGStab
   Linear System Preconditioning = ILU0
   Linear System Convergence Tolerance = Real 1.0e-12
   Linear System Abort Not Converged = False
   Linear System Residual Output = 1500

! equation is linear if no min/max
   Nonlinear System Max Iterations = 50
   Nonlinear System Convergence Tolerance  = 1.0e-6
   Nonlinear System Relaxation Factor = 1.00


  Stabilization Method = stabilized
  Apply Dirichlet = Logical False

!!  the convection velocity (mean horizontal velocity)
     Flow Solution Name = String "SSAVelocity"
End

!! This solver is just used to update Zs (look for the value of Zs in Body forces
Solver 3
   Equation = "UpdateExport"
   Procedure = "ElmerIceSolvers" "UpdateExport"
   Variable = -nooutput "dumy"

   Exported Variable 1 = -dofs 1 "Zs"
   Exported Variable 2 = -dofs 1 "Zb"
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Equation 1
  Active Solvers(3) = 1 2 3 
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Boundary Condition 1
  Target Boundaries = 1
  

End

! Periodic Right
Boundary Condition 2
  Target Boundaries = 2
  Periodic BC = 4 
  Periodic BC Translate(2) = Real $L 0.0  
  Periodic BC SSAVelocity 1  = Logical True
  Periodic BC SSAVelocity 2  = Logical True
  Periodic BC H  = Logical True
  
End

Boundary Condition 3
  Target Boundaries = 3

  Periodic BC = 1 
  Periodic BC Translate(2) = Real 0.0 $L 
  Periodic BC SSAVelocity 1  = Logical True
  Periodic BC SSAVelocity 2  = Logical True
  Periodic BC H  = Logical True

End

Boundary Condition 4
  Target Boundaries = 4
End