• Solver Fortran File: IDSSolver.f90
• Solver Name: IDSSolver
• Required Output Variable(s): IDSHead, IDSHead Residual, IDSHead Homologous and IDSHead Pressure
• Required Input Variable(s): None
• Optional Output Variable(s): None
• Optional Input Variable(s): IDS Head Upper Limit (required if the upper limit is used)

This solver treat the diffusion equation with a user defined upper limit.

The required keywords in the SIF file for this solver are given bellow. The IDSSolver can be used alone, coupling between the two layer is treated in the EPLSolver section

The hydrological system is only treated at the bed, it requires then a new equation, we keep the Material an Body Force section of the ice.

Body 2
  Name = "hydrological system"
  Equation = 2
  Material = 1
  Body Force = 1
  Initial Condition = 2
End

! Initial condition for the hydrology
Initial Condition 2
  IDSHead = real 0.0
End

Constants
  Water Compressibility = Real 5.04e-4  !MPa-1
End

Only the parameters which are needed for the treatment of the hydrology are given here, you should add it to your existing Body Forces and Material.

Body Force 1
  Flow BodyForce 1 = 0.0
  Flow BodyForce 2 = 0.0
  Flow BodyForce 3 = MATC "-9.81*(31556926.0)^(2.0)"

  IDSHead Source Flux = Real 2.0
End

Material 1
! General Hydrology Parameters
  Water Density = Real MATC "1000.0*1.0E-06*(31556926.0)^(-2.0)"

! IDS Solver
  IDS Transmitivity = Real 5.0e2
  IDS Porosity = Real 0.4
  IDS Thickness = Real 20.0
  IDS Compressibility = Real 1.0e-2

!Upper limit at the flotation limit
  IDSHead Upper Limit = Variable Depth, coordinate 3
      Real matc "tx(1)+tx(0)*0.91"
End

Solver 1
 Equation = "IDS Equation"

  Procedure = "ElmerIceSolvers" "IDSSolver"
  Variable = IDSHead
  Variable DOFs = 1

  Steady State Convergence Tolerance = Real 1.0E-5

  Linear System Solver = Direct
  Linear System Direct Method = umfpack
  Linear System Convergence Tolerance = Real 1.0E-7
  Linear System Residual Output = integer 1

  Nonlinear System Max Iterations = Integer 100
  Nonlinear System Convergence Tolerance = Real 1.0E-6
  Nonlinear System Relaxation Factor = Real 1.0

  !This deals with the upper limit (enabled if TRUE)
  Apply Dirichlet = Logical TRUE

  Exported Variable 1 = String "IDSHead Residual"
  Exported Variable 2 = String "IDSHead Homologous"
  Exported Variable 3 = String "IDSHead Pressure"

End

Equation 2
 Active Solvers (1) = 1
End

The boundary condition of the hydrological model should be applied on a 1D boundary located at the corner between the side and bed of the mesh.

Boundary Condition 4
  Name = "Lower frame"
  Target Boundaries = 4
  
! Flux condition on the borders of the hydrological domain
! Zero flux is not a necessary input as it is the natural 
! boundary condition of the system

  IDSHead Flux BC = Logical True 
  IDSHead Water Flux = Real 0.0
End

Boundary Condition 5
  Name = "Glacier snout"
  Target Boundaries = 5
  
! Take care to choose a value bellow or equals to the upper 
1 limit of the water head
  
  IDSHead = variable coordinate 3, depth
    real matc "tx(0)+0.91*tx(1)"
End

Two basic tests can be found in [ELMER_TRUNK]/elmerice/Tests/Hydro_SedOnly and [ELMER_TRUNK]/elmerice/Tests/Hydro_Coupled.

When used this solver can be cited using the following reference :
de Fleurian, B.; Gagliardini, O.; Zwinger, T.; Durand, G.; Le Meur, E.; Mair, D. & Råback, P. A double continuum hydrological model for glacier applications The Cryosphere, 2014, 8, 137-153