Age/Depth Relation

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This page explains how to use the general AdvectionReactionSolver to get Age/Depth relation. Mind, that the AdvectionReactionSolver is not part of the Elmer release, but only in the SVN distribution. It solves the general equation

dA/dt + u dA/dx + v dA/dy + w dA/dz + gamma A = source

The Solver section looks as

Solver 8
  Equation = "AdvReact"
  Exec Solver = "After Timestep"
  Procedure = File "AdvectionReaction" "AdvectionReactionSolver"
  ! this is the DG variable, which is not part of the output
  Variable =  -nooutput "DGAge"
  ! this tells that the solver is run on DG mesh
  Discontinuous Galerkin = Logical True
  ! the solver can account for upper and lower limits of the variable
  ! imposed by formulation of an variational inequality (VI)
  ! next line switches the VI to be accounted for
  Limit Solution = Logical True

  Linear System Solver = Iterative
    Linear System Iterative Method = BiCGStab
  Linear System Max Iterations  = 1000
  Linear System Preconditioning = ILU1
  Linear System Convergence Tolerance = 1.0e-06
  ! Variational inequality makes it a non-linear problem
  Nonlinear System Max Iterations = 40
  Nonlinear System Min Iterations = 2
  Nonlinear System Convergence Tolerance = 1.0e-04

  ! This is the variable that is used to interpolate
  ! the DG solution to the regular FEM mesh in order
  ! to get a correct output
  Exported Variable 1 = Age
  Exported Variable 1 DOFS = 1

The source in case of the age/depth equation is 1 (da/dt + u da/dx + ... = 1)

Body Force 1
  DGAge Source = Real 1.0  ! result in years

Initial and boundary conditions are then being set for the DG variable and not the exported one!

Initial Condition 1
  DGAge = Real 0.0

! only Dirichlet BC can be set
! the solver automatically uses this
! condition only on inflow boundaries
! outflow boundaries are ignored
Boundary Condition 2
  Name = "surf"
  Target Boundaries = 2
  Body ID = 2
  ! fresh snow or ice
  DGAge = Real 0.0

! a suggestion for a trick at no-slip BC's to
! keep the age in bounds
Boundary Condition 1
   Name = "bedrock"
   Normal-Tangential Velocity = True
  ! normal outflow velocity set to a very small value
  ! in order to avoid infinitely large age values
  Velocity 1 = Real 1.0e-06 (a micro-meter per year)
  ! no-slip tangential
  Velocity 2 = Real 0.0
  Velocity 3 = Real 0.0

Just make sure that a free surface can have both, inflow and outflow.
NB: If you have a model for re-freezing at the bedrock, you also should set a DGAge = Real 0.0 on this boundary.

The Material section contains a zero reaction rate as well as the upper/lower limit for the DG variable

Material 1

 ! this has to be sometimes set in diagnostic
 ! runs to avoid infinite [actually O(1/machine precission)]
 ! ages at stagnation points in the flow field
 DGAge Upper Limit = Real 100000

 ! well, no ice from the future
 ! anyways, if you have a well behaving velocity field
 ! you should not be in need of that constraint
 DGAge Lower Limit = Real 0

 !this would be a reaction rate,
 ! in our case zero
 DGAge Gamma = Real 0.0