This is an old revision of the document!
GlaDSCoupledSolver.F90
and GlaDSchannelSolver.F90
GlaDSCoupledSolver
, GlaDSsheetThickDummy
and GlaDSchannelOut
Hydraulic Potential
, Sheet Thickness
and Channel Area
Vclose
, Wopen
, Water Pressure
, Effective Pressure
, Sheet Discharge
, Sheet Storage
and Channel Flux
Zb
The complete description of the equations solved by the GlaDS solver can be found in Werder et al. (2013). The implementation follows exactly these equations, except that optionally the hydraulic potential can be computed at the top of the water sheet instead than at the bed (keyword: Neglect Sheet Thickness in Potential
).
The GlaDS solver solves for the hydraulic potential, the water sheet thickness and the cross-sectional area of the channels. Whereas the two first variables are nodal variable and define continuous fields, the Channel area is a discrete field only defined on the edge of the elements.
The GlaDS model is composed of three solvers:
GlaDSCoupledSolver
is the main solver and couple the solve of the 3 main variables Hydraulic Potential
, Sheet Thickness
and Channel Area
. Detail on the keywords for this solver are given below. GlaDSsheetThickDummy
is just a solver to declare the Sheet Thickness
variable as a primary variable.GlaDSchannelOut
has two functions: declare that the Channel Area
variable is an edge variable (Element = “n:0 e:1”
) and create output vtk files for edge variables.
Currently (June 2017), GlaDSchannelOut
doesn't support parallel simulation. These solvers only work in transient. They can be executed either on a 2d plane view mesh defining the bedrock or on the boundary of a 3d mesh. More details about the specificity of the solvers are given below.
The GlaDS solvers depend on a lot of physical parameters. The SIF example given here is from the test A1 of SHMIP. The main parameters to be defined in the Material
section are:
! For the sheet Sheet Conductivity = Real $Ks Sheet flow exponent alpha = Real $alphas Sheet flow exponent beta = Real $betas Englacial Void Ratio = Real $ev Bedrock Bump Length = Real $lr Bedrock Bump High = Real $hr Sheet Closure Coefficient = Real $Ar ! For the Channels Channel Conductivity = Real $Kc Channel flow exponent alpha = Real $alphac Channel flow exponent beta = Real $betac Channel Closure Coefficient = Real $Ac Sheet Width Over Channel = Real $lc Pressure Melting Coefficient = Real $Ct Water Heat Capacity = Real $Cw ! Coupling with ice flow and glacier geometry Sliding Velocity = Real $ub Ice Normal Stress = Variable Coordinate 1 Real MATC "rhoi*gravity*H(tx)"
In the Body Force
section, one can set a water input source:
Body Force 1 Hydraulic Potential Volume Source = Real $Source End
GlaDSCoupledSolver
solves for the three variables Hydraulic Potential
, Sheet Thickness
and Channel Area
in a coupled way. Equations for the Hydraulic Potential
and Channel Area
are non linear. Only the equation for the Hydraulic Potential
needs to solve a system. The two others are local and can be solved either explicitely, implcitely or using the Crank-Nicholson method.
Solver 1 Equation = "GlaDS Coupled sheet" Procedure = "./GlaDS" "GlaDSCoupledSolver" Variable = -dofs 1 "Hydraulic Potential" Activate Channels = Logical True ! activate or not the development of channels Activate Melt from Channels = Logical True ! activate or not the growth of channels by melt Neglect sheet Thickness in Potential = Logical True ! compute the hydraulic potential at the top of the water sheet (''False'') or at the bed (''True'') ! choices are EXPLICT, CRANK-NICHOLSON, IMPLICIT Channels Integration method = String "Crank-Nicholson" Sheet Integration method = String "Implicit" Exported Variable 1 = -dofs 1 "Vclose" Exported Variable 2 = -dofs 1 "Wopen" Exported Variable 3 = -dofs 1 "Normal Stress" Exported Variable 4 = -dofs 1 "Water Pressure" Exported Variable 5 = -dofs 1 "Effective Pressure" Exported Variable 6 = -dofs 2 "Sheet Discharge" Exported Variable 7 = -dofs 1 "Sheet Storage" Exported Variable 8 = -dofs 1 "Zs" Exported Variable 9 = -dofs 1 "Zb" Linear System Solver = Direct Linear System Direct Method = umfpack Nonlinear System Max Iterations = 10 Nonlinear System Convergence Tolerance = 1.0e-6 Nonlinear System Relaxation Factor = 1.00 Coupled Max Iterations = Integer 10 Coupled Convergence Tolerance = Real 1.0e-3 Steady State Convergence Tolerance = 1.0e-03 End
An example using the GlaDS Solver can be found in [ELMER_TRUNK]/elmerice/examples/GlaDS
.
The description of the GlaDS model is in:
Werder M.A., I.J. Hewitt, C.G. Schoof and G.E. Flowers, 2013. Modeling channelized and distributed subglacial drainage in two dimensions. Journal of Geophysical Research: Earth Surface, 118(4), 2140-2158.