ismip_SSA_1D.sif

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!                                          !!
!! ISMIP-HOM E020 (1D) solved in prognostic !!
!!   using SSA and thickness solvers        !!
!!                                          !!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


$Step = "SSA_1D"
$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

  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

! bottom where SSA and Thickness equations are solved
Body 2
  Equation = 2
  Body Force = 1
  Material = 1
  Initial Condition = 1
End


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Initial Condition 1
  SSAVelocity  = Real 0.0

  H = Real 1000.0

  Zs = Variable Coordinate 1
    Real MATC "-tx*tan(Slope)"
  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 $gravity

  Zs = Variable Zb , H
     REAL MATC "tx(0)+tx(1)"
End

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

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


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

  SSA Friction Law = String "linear"
  SSA Friction Parameter = Variable coordinate 1 
     Real  MATC "1.0e-3*(1.0 + sin(2.0*pi* tx(0) / L))  

End
 
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solver 1
  Equation = "SSA"
  Variable = -dofs 1 "SSAVelocity"

  Procedure = "ElmerIceSolvers" "SSABasalSolver"

  Linear System Solver = Direct         
  Linear System Direct Method = umfpack

  Nonlinear System Max Iterations = 50
  Nonlinear System Convergence Tolerance  = 1.0e-10
  Nonlinear System Newton After Iterations = 5
  Nonlinear System Newton After Tolerance = 1.0e-06

  Steady State Convergence Tolerance = Real 1.0e-3
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

   Nonlinear System Max Iterations = 50
   Nonlinear System Convergence Tolerance  = 1.0e-6
   Nonlinear System Relaxation Factor = 1.00

   Steady State Convergence Tolerance = 1.0e-03

  Stabilization Method = stabilized
  Apply Dirichlet = Logical False

  !! you can give the  name of 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

!!! dumy here, just to have a solver in body 1
Solver 4
  Exec Solver = never
    Equation = "Navier-Stokes"

      Stabilization Method = String Bubbles
        Flow Model = Stokes
End

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

Equation 1
  Active Solvers(1) = 4
End

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

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Boundary Condition 1
  Target Boundaries = 1
  
  Body Id = 2

End

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

Boundary Condition 3
  Target Boundaries = 3

End

Boundary Condition 4
  Target Boundaries = 4
End