This is an old revision of the document!
important changes have been made in SSABasalSolver; This doc applies from Rev. 6440
SSASolver.f90
SSABasalSolver
, (2) GetMeanValueSolver
and (3) SSASolver
SSAVelocity
Mean Viscosity
and Mean Density
SSAFlow
Zb
, Zs
Depth
Depth
, FreeSurfGrad1
, FreeSurfGrad2
and SSABasalFlow
The SSABasalSolver
solve the classical SSA equation, it has been modified in Rev. 6440 to be executed either on a grid of dimension lower than the problem dimension itself (i.e. the top or bottom grid of a 2D or 3D mesh for a SSA 1D or 2D problem), or on a grid of the same dimension of the problem (i.e. 2D mesh for a 2D plane view SSA solution).
It will work on a 3D mesh only if the mesh as been extruded along the vertical direction and if the base line boundary conditions have been preserved (to impose neumann conditions).
The mandatory input variables are the bottom surface elevation and top surface elevation variables called Zb and Zs, respectively.
For the Flow law the SSA solver use a “power-law” formulation and use the keywords 'Viscosity Exponent', 'Critical Shear Rate', and “Mean Viscosity”. It Doesn't work with the build-in Glen's flow law (TODO).
Newton linearistaion of the viscosity can be used usning the keywords 'Nonlinear System Newton After Tolerance' and/or
'Nonlinear System Newton After Iterations'. It is automatically reset to False at the beginning of a new iteration.
The “Mean Density” and “Mean Viscosity”, if not uniform along the vertical direction, can be computed using the GetMeanValueSolver
routine or the “StucturedProjectToPlane” solver (prefered solution).
Contrary to the NS solver, the gravity must be orientated along the z-axis and it taken form the value of
Flow BodyForce 2
for a SSA-1D problem or Flow BodyForce 3
for a SSA-2D problem.
A Neumann condition on the lateral boundaries can be applied with the keyword “Calving front = Logical True” in the Bounadry condition section. The condition is : 0.5 * g * (rho_ice * h^2 - rho_water * h_im^2) where
Flow BodyForce i“
- rho_ice is the ice “Mean Density”
- rho_water is “water density” taken from the “constants” section (or default=1.03225e-18)
- h is the front thickness computed as Zs-Zb
- h_im is the thickness below sea level computed as “Sea Level - Zb”, where “Sea Level” is taken from the “constants” section (or default=0.0).
Note that in the absence of explicit boundary condition (no dirichlet condition or “Calving front = Logical True” not found) the natural boundary condition is force equilibrium (rho_ice * h^2 = rho_water * h_im^2).
The slip coefficient coefficient values are imposed in the Material section with the keywords
“SSA slip coefficient i = Real …” with i=1,2
The SSA velocities and pressure can be use, for example, as initial conditions for the Stokes Solver.
When the SSA solution is computed on a boundary of a mesh of dimension larger than the SSA problem (e.g. a 3D mesh for a SSA-2D problem), the SSA solution computed on the boundary
- can be exported on the whole mesh using (i) The “StructuredProjectToPlane” solver (prefered solution) or (ii) the
SSASolver'' routine The required keywords in the SIF file for this solver are:
Solver 2 Equation = "SSA-IntValue" Procedure = File "ElmerIceSolvers" "GetMeanValueSolver" Variable = -nooutput String "Integrated variable" Variable DOFs = 1 Exported Variable 1 = String "Integrated Viscosity" Exported Variable 1 DOFs = 1 Exported Variable 2 = String "Mean Density" Exported Variable 2 DOFs = 1 Linear System Solver = Direct Linear System Direct Method = umfpack Steady State Convergence Tolerance = Real 1.0e-3 End ! Solver 3 Equation = "SSA-BasalVelo" Procedure = File "ElmerIceSolvers" "SSABasalSolver" Variable = String "SSABasalFlow" Variable DOFs = 2 ! 2 in 3D Linear System Solver = Direct Linear System Direct Method = umfpack Nonlinear System Max Iterations = 100 Nonlinear System Convergence Tolerance = 1.0e-5 Nonlinear System Relaxation Factor = 1.00 Steady State Convergence Tolerance = Real 1.0e-3 End Solver 4 Equation = "SSA Velocity" Procedure = File "ElmerIceSolvers" "SSASolver" Variable = -nooutput String "varSSA" Variable DOFs = 1 Exported Variable 1 = String "SSAFlow" Exported Variable 1 DOFs = 4 ! 3 in 2D, 4 in 3D Linear System Solver = Direct Linear System Direct Method = umfpack Steady State Convergence Tolerance = Real 1.0e-3 End ! SSA equation only solved on the bedrock boundary Equation 2 Active Solvers(1) = 3 End !!! bedrock Boundary Condition 5 Target Boundaries = 5 Body Id = Integer 2 SSAFlow 1 = Equals SSABasalFlow 1 SSAFlow 2 = Equals SSABasalFlow 2 SSAFlow 3 = Real 0.0e0 SSA Slip Coefficient 1 = Variable Coordinate 1, Coordinate 2 Real MATC "1000.0e-6*(1.0+sin(2.0*pi*tx(0)/L)*sin(2.0*pi*tx(1)/L))" SSA Slip Coefficient 2 = Variable Coordinate 1, Coordinate 2 Real MATC "1000.0e-6*(1.0+sin(2.0*pi*tx(0)/L)*sin(2.0*pi*tx(1)/L))" End !!! Upper free surface Boundary Condition 6 Target Boundaries = 6 Depth = Real 0.0 Integrated Viscosity = Real 0.0 Mean Density = real 0.0 SSAFlow 4 = Real 0.0 ! p=0 at the bottom End
If one wants to solve the SSA + SIA, the sif will read:
Solver 4 Equation = "SIA Velocity" Procedure = File "SIASolver" "SIASolver" Variable = -nooutput String "varSIA" Variable DOFs = 1 Exported Variable 1 = String "SIAFlow" Exported Variable 1 DOFs = 4 ! 3 in 2D, 4 in 3D Linear System Solver = Direct Linear System Direct Method = umfpack Steady State Convergence Tolerance = Real 1.0e-3 End !!! bedrock Boundary Condition 5 Target Boundaries = 5 Body Id = Integer 2 SIAFlow 1 = Equals SSABasalFlow 1 SIAFlow 2 = Equals SSABasalFlow 2 SIAFlow 3 = Real 0.0e0 ... End !!! Upper free surface Boundary Condition 6 Target Boundaries = 6 ... SIAFlow 4 = Real 0.0 ! p=0 at the bottom End
If the front is in contact with the ocean, this boundary condition reads:
$rhow = 1000.0/(1.0e6*yearinsec^2) Constants Water Density = Real $rhow End !!! BC Lateral Ice-Shelf (air or sea contact) Boundary Condition 2 Target Boundaries = 2 Calving Front = Logical True End
For examples look in your elmer source distribution under [ELMER_TRUNK]/elmerice/examples/Test_SSA