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problems:rheology [Elmer/Ice Wiki]

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problems:rheology [2012/11/23 20:22]
gag [Glen's flow law]
problems:rheology [2021/07/12 07:06] (current)
gagliar [Glen's flow law]
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 ==== Glen's flow law ==== ==== Glen's flow law ====
-This is a SIF entry for Glen's flow law (after: Paterson, W. S. B. 1994. ''The Physics of Glaciers.'' Pergamon Press, Oxford etc., 3rd edt.) using the built-in Elmer viscosity law (recommended, as it is evaluated at Gauss-points):+This is a SIF entry for Glen's flow law (after: Cuffey and Paterson, 2010. ''The Physics of Glaciers.'' Pergamon Press, Oxford etc., 4th edt.) using the built-in Elmer viscosity law (recommended, as it is evaluated at Gauss-points):
 <code> <code>
-! Glen's flow law (using Glen) +! Define some constant at the top of the SIF file (using LUA) 
-!---------------- +! Define the parameter in MPa - a - m 
-! viscosity stuff +#yearinsec = 365.25*24*60*60 
-!---------------- +#rhoi = 900.0/(1.0e6*yearinsec^2) 
-  Viscosity Model = String "Glen" +#rhow = 1000.0/(1.0e6*yearinsec^2) 
-! Viscosity has to be set to a dummy value +#gravity = -9.81*yearinsec^2 
-! to avoid warning output from Elmer + 
-  Viscosity = Real 1.0 +! Prefactor from Cuffey and Paterson (2010) in MPa^{-3} a^{-1} 
 +#A1 = 2.89165e-13*yearinsec*1.0e18 
 +#A2 = 2.42736e-02*yearinsec*1.0e18 
 +#Q1 = 60.0e3 
 +#Q2 = 115.0e3 
 + 
 + 
 +Material 1 
 +  Density = Real #rhoi 
 +   
 +  ! Glen's flow law (using Glen) 
 +  !---------------- 
 +  ! viscosity stuff 
 +  !---------------- 
 + 
 +  Viscosity Model = String "glen
 +  Viscosity = 1.0 ! Dummy but avoid warning output
   Glen Exponent = Real 3.0   Glen Exponent = Real 3.0
-  Critical Shear Rate = Real 1.0e-10 +
-! Rate factors (Paterson value in MPa^-3a^-1) +
-  Rate Factor 1 = Real 1.258e13   +
-  Rate Factor 2 = Real 6.046e28 +
-! these are in SI units - no problem, as long as +
-! the gas constant also is  +
-  Activation Energy 1 = Real 60e3 +
-  Activation Energy 2 = Real 139e3   +
-  Glen Enhancement Factor = Real 1.0 +
-! the variable taken to evaluate the Arrhenius law +
-! in general this should be the temperature relative +
-! to pressure melting point. The suggestino below plugs +
-! in the correct value obtained with TemperateIceSolver +
-  Temperature Field Variable = String "Temp Homologous" +
-! the temperature to switch between the  +
-! two regimes in the flow law+
   Limit Temperature = Real -10.0   Limit Temperature = Real -10.0
-! In case there is no temperature variable +  Rate Factor 1 = Real #A1 
-  !Constant Temperature = Real -10.0+  Rate Factor 2 = Real #A2 
 +  Activation Energy 1 = Real #Q1 
 +  Activation Energy 2 = Real #Q2 
 +  Glen Enhancement Factor = Real 1.0 
 +  Critical Shear Rate = Real 1.0e-10 
 + 
 +  Constant Temperature = Real -1.0  
 +End
 </code> </code>
  
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 This Material section gives the law with a fixed rate factor: This Material section gives the law with a fixed rate factor:
 <code> <code>
 +Material 1
 ! Glen's flow law (using Glen) ! Glen's flow law (using Glen)
 !----------------- !-----------------
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   Arrhenius Factor = Real $1.0E-16 * 1.0E18   Arrhenius Factor = Real $1.0E-16 * 1.0E18
   Glen Enhancement Factor = Real 1.0   Glen Enhancement Factor = Real 1.0
 +End
 </code> </code>
  
-This is a SIF entry for Glen's flow law (after: Paterson, W. S. B. 1994. ''The Physics of Glaciers.'' Pergamon Press, Oxford etc., 3rd edt.) using the old power law (MATC function):+This is a SIF entry for Glen's flow law (after: Paterson, W. S. B. 1994. ''The Physics of Glaciers.'' Pergamon Press, Oxford etc., 3rd edt.) using the old power law (MATC function) (Not recommended, use build-in implementation of Glen's flow law - first solution on this page):
 <code> <code>
 !! Glen's flow law (using power law) !! Glen's flow law (using power law)
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 Viscosity Exponent = $1.0/3.0 Viscosity Exponent = $1.0/3.0
 </code> </code>
 +
 +Strictly speaking the homologous temperature should be used as input to the Glen function above, but if homologous temperature is not readily available then using temperature (in Celsius) is a good approximation (which deteriorates for thicker glaciers/ice sheets).
  
 Be very careful in choosing the correct value of the critical shear rate. A too high value leads to a way too soft ice at low shear rates, a too low value can have consequences on the numerical stability (singularity of shear thinning fluid at zero shear). Be very careful in choosing the correct value of the critical shear rate. A too high value leads to a way too soft ice at low shear rates, a too low value can have consequences on the numerical stability (singularity of shear thinning fluid at zero shear).
  
  
-An example using Glen's flow law can be downloaded {{:problems:test_glen_2d.tar.gz|here}}.+An example using Glen's flow law can be found in ''[ELMER_TRUNK]/elmerice/examples/Test_Glen_2D''..
  
 ==== Anisotropic Ice ==== ==== Anisotropic Ice ====
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 The rheology of **porous ice**, namely firn and snow, is represented using the porous law proposed by Gagliardini and Meyssonnier (1997). This law is implemented in Elmer/Ice in the [[solvers:porous|Porous Solver]]. Density evolution can be computed from the mass conservation equation.  The rheology of **porous ice**, namely firn and snow, is represented using the porous law proposed by Gagliardini and Meyssonnier (1997). This law is implemented in Elmer/Ice in the [[solvers:porous|Porous Solver]]. Density evolution can be computed from the mass conservation equation. 
  
 +==== Damage ==== 
 +Damage is accounted for through the enhancement factor. Damage evolution is modelled following the approach in Krug et al. (2014). More information can be found [[userfunctions:damage|here]].
problems/rheology.1353702145.txt.gz · Last modified: 2012/11/23 20:22 by gag
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