ismip_weertman2.sif

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!                                       !!
!! Test for Weertman friction law        !!
!!                                       !!
!! From test ISMIP-HOM B020              !!
!!                                       !!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! This is a variation related to internal user defined friction law
! implemented in IncompressibleNSVec. With these ideas other models could
! be easily implemented with the same philosophy.
! P.R. 3.2.2022
!
!check keywords warn
!echo on
$L = 20.0e3
$Slope = 0.5 * 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)
$beta = 0.02

Header
  Mesh DB "." "rectangle"
End

Constants
! No constant Needed
End

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

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

!  Post File = "ismip_weertman.vtu"
  max output level = 7   
End

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

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Initial Condition 1
  Pressure = Real 0.0 
  Velocity 1 = Real 0.0 
  Velocity 2 = Real 0.0 
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Body Force 1
  Flow BodyForce 1 = Real 0.0                          
  Flow BodyForce 2 = 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

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solver 1  
  Equation = "MapCoordinate"
  Procedure = "StructuredMeshMapper" "StructuredMeshMapper"
  Active Coordinate = Integer 2

  Mesh Velocity Variable = String "dSdt"
  Mesh Update Variable = String "dS"
  Mesh Velocity First Zero = Logical True
End

Solver 2
  Equation = "Normal vector"
  Procedure = "ElmerIceSolvers" "ComputeNormalSolver"
  Variable = -dofs 2 "Normal Vector"   
  Optimize Bandwidth = Logical False 
  ComputeAll = Logical False
End

Solver 3
  Equation = "Navier-Stokes"

  Procedure = "IncompressibleNSVec" "InCompressibleNSSolver"
  Exported Variable 1 = -dofs 1 "dSdt" 
  Exported Variable 2 = -dofs 1 "dS" 
  
  Stabilization Method = String Bubbles
  Flow Model = Stokes

  Linear System Solver = Direct         
  Linear System Direct Method = umfpack

  Nonlinear System Max Iterations = 100
  Nonlinear System Convergence Tolerance  = 1.0e-6
  Nonlinear System Newton After Iterations = 5
  Nonlinear System Newton After Tolerance = 1.0e-02
  Nonlinear System Relaxation Factor = 1.00
  Nonlinear System Reset Newton = Logical True

  Steady State Convergence Tolerance = Real 1.0e-3
End


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

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

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Bedrock
Boundary Condition 1
  Target Boundaries = 1
  Normal-Tangential Velocity = Logical True
  Flow Force BC = Logical True
    
  Velocity 1 = Real 0.0
!  Slip Coefficient 2 =  Variable Coordinate 1
!    Real Procedure "ElmerIceUSF" "Sliding_Weertman"

! These are generic for 1)-3)
! If we know that normal velocity is zero by construction no need
! to reduce it from the velocity field. 
!  Friction Normal Velocity Zero = Logical True
! Cut-off such that argument is not smaller than this
  Friction Linear Velocity = Real 1.0e-4 

! 1) Internal Weertman model 
!  Weertman Friction Coefficient = Real $beta         
!  Weertman Exponent = Real $1.0/n

! 2) User defined friction coefficient with F90 - Weertman model
! Friction Coefficient = Variable "dummy"
!    Real Procedure "MyModule" "MyWeertman"

! 3) User defined friction coefficient with MATC - Weertman model
$alpha=1.0/n-1.0
  Friction Coefficient = Variable "dummy"
    Real MATC "min(beta*(tx^alpha) 1.0e20)"

  ComputeNormal = Logical True

  Bottom Surface = Variable Coordinate 1
    Real MATC "-tx*tan(Slope)-1000.0+500.0*sin(2.0*pi*tx/L)"
End

! Periodic Right
Boundary Condition 2
  Target Boundaries = 2
  Periodic BC = 4 
  Periodic BC Translate(2) = Real $L 0.0  
  Periodic BC Velocity 1  = Logical True
  Periodic BC Velocity 2  = Logical True
  Periodic BC Pressure  = Logical True
  
  ComputeNormal = Logical False
End

! Upper Surface
Boundary Condition 3
  Target Boundaries = 3
  ComputeNormal = Logical False

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

! Periodic Left
Boundary Condition 4
  Target Boundaries = 4
  ComputeNormal = Logical False
End

Solver 3 :: Reference Norm = 5.67318925E+01
! Norm of original test: 56.70374