AdjointSSA_SSASolver.md

AdjointSSA : Direct Solver {#ssa_direct_solver}

Module name: AdjointSSA_SSASolver.F90 Module subroutines: AdjointSSA_SSASolver Module authors: Fabien Gillet-Chaulet (IGE-Grenoble) Document authors: Fabien Gillet-Chaulet Document edited: 28/04/2020

Solver Variable:

• SSAVelocity : horizontal velocity

Required input variables:

• Zb: bottom surface elevation

• Zs: top surface elevation

• [Optional - see below] GroundedMask : mask for grounded (>=0) or floating (<0) ice

• [Optional - see below] bedrock : bed elevation

Introduction

This solver solves the classical SSA equation for the horizontal velocity.

It is very similar to the legacy Elmer/Ice SSABasalSolver. However it is separated to derive the adjoint code (AdjointSSA : Gradient Solver) and make sure that they are consistent.

Keywords

Solver Section:

  Solver *id*
  Equation = "SSA"

  !# dimension 1 or 2 for flowline or 2D
   Variable = -dofs 2 "SSAVelocity"

   Procedure = "ElmerIceSolvers" "AdjointSSA_SSASolver"

  !# Set true to set friction to 0 when ice is floating
  !   Require: GroundedMask and Bedrork variables
  Sub-Element GL parameterization = logical True
  !# You can set the number of IP points to evaluated the friction in the
  !   first floating element
  GL integration points number = Integer 20

  !# Keywords related to linear system
  Linear System Solver = ...

  !# Keywords related to non-linear iterations 
  !  for the accuracy of the gradient computation
  !   Newton has to be used if the problem is non linear
   Nonlinear System Max Iterations = Integer ...
   Nonlinear System Convergence Tolerance  = Real ....
   Nonlinear System Newton After Iterations = Integer ...
   Nonlinear System Newton After Tolerance = Real ...
   Nonlinear System Relaxation Factor = 1.00


  End

Material Properties:

  Material *id*

  Viscosity Exponent = Real ....
  Critical Shear Rate = Real ....

  SSA Mean Viscosity = Real ...
  SSA Mean Density = Real ...

 !# Friction law (linear or weertamn)
  SSA Friction Law = String ...
 !# Friction coefficient
 !  it is set to 0 automatically for floating ice if 
 !    Sub-Element GL parameterization = logical True [see above]
  SSA Friction Parameter = Real ...

 !# Keywords related to Weertman
 !# SSA Friction Exponent m 
  SSA Friction Exponent = Real
 ! Min velocity for linearisation where ub=0
  SSA Friction Linear Velocity = Real ....

Constants:

Constants
! Used for Neumann condition
  Water Density = Real ....
  Sea Level = Real ...
End

Body Forces:

!# gravity for BodyForce 2 (1D-case) or BodyForce 3 (2D plane view case)
Body Force *id*
  Flow BodyForce 1 = Real 0.0
  Flow BodyForce 2 = Real 0.0
  Flow BodyForce 3 = Real $gravity
End

Boundary Conditions:

Boundary Condition 1 
! Dirichlet condition
  SSAVelocity 1 = Real ...
  SSAVelocity 2 = Real ...
End
Boundary Condition 1 
! Neumann Condition
  Calving Front = Logical True
End

Tests and Examples

• See examples for the SSA inverse methods