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userfunctions:coulomb [2012/11/15 02:14]
gag [General Description]
userfunctions:coulomb [2015/12/02 12:24] (current)
gag [General Description]
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 ==== General Informations ==== ==== General Informations ====
-  * **USF Fortran File:​** ​//USF_Sliding.f90// +  * **USF Fortran File:​** ​''​USF_Sliding.f90''​ 
-  * **USF Name:​** ​//Friction_Coulomb// +  * **USF Name:​** ​''​Friction_Coulomb''​ 
-  * **Required Input Variable(s):​** A //Flow Solution// in //Flow Solution Name////Normal Vector////Stress//+  * **Required Input Variable(s):​** A ''​Flow Solution'' ​in ''​Flow Solution Name''​''​Normal Vector''​''​Stress''​ or the ''​Effective Pressure''​ variable.
  
  
 ==== General Description ==== ==== General Description ====
-The file //USF_Sliding.f90// contains ​two user functions to apply non-linear friction at the base of glacier.  ​+The file ''​USF_Sliding.f90'' ​contains ​three user functions to apply non-linear friction at the base of glacier.  ​
  
-The first user function (//Sliding_Weertman//) is a non-linear Weertman-type friction law and is described [[:​userfunctions:​weertman|here]]. The second user function (//Friction_Coulomb//) is a non-linear water pressure dependant friction law, as proposed by Schoof (2005) and Gagliardini et al. (2007), and is presented in this page.+The first user function (''​Sliding_Weertman''​) is a non-linear Weertman-type friction law and is described [[:​userfunctions:​weertman|here]]. The second user function (''​Friction_Coulomb''​) is a non-linear water pressure dependant friction law, as proposed by Schoof (2005) and Gagliardini et al. (2007), and is presented in this page. The third user function (''​Sliding_Budd''​) is described [[:​userfunctions:​budd|here]] and is from Budd et al 1984 (Annals of Glaciology 5, page 29-36)
   ​   ​
  
-The friction law in //​Friction_Coulomb//​ is of the form: +The friction law in //​Friction_Coulomb//​ is of the form:\\ 
-<​m> ​ +<​m> ​ tau_b = C.N {[{ {chi {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n} . u_b  </​m>​\\ 
-  tau_b = C.N.[{ {ub^{-n} }/ {(1 + a.X^q)} }]^{1/n} . ub +where \\ 
-</m>+<​m> ​ a = {(q - 1)^{q-1}}/​{q^q} ​ </​m>​\\ 
 +and\\ 
 +<​m> ​ chi = {u_b}/{C^n N^n A_s}  ​</m>\\
  
-Parameters: Friction Law Sliding Coefficient ​     -> As  +The //Slip Coefficient//​ in Elmer is then given as\\ 
-!             Friction Law Post-Peak Exponent ​        ​-> q >= 1 +<​m> ​ C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/​n} ​ </​m>​\\ 
-!             Friction Law Maximum Value            -> C ~ max bed slope   ​ +When  <​m>​u_b < u_{t0}</​m>,​ <​m>​u_b</​m>​ in the previous equation is replaced by <​m>​u_{t0}</​m>​. 
-!             Friction Law Linear Velocity ​         -> ut0 + 
-!             ​Friction Law PowerLaw ​Exponent ​       -> m = (n Glen's law) + 
-+The parameters to be given are:\\ 
-!             Water Pressure (BC)    (Compressive - positive) +  * ''​Friction Law Sliding Coefficient'' ​     ​-> ​<​m>​A_s</​m>​ 
-+  * ''​Friction Law Post-Peak Exponent'' ​      -> <m>q >= 1</m> 
- tau_b = C.N.[ X . ub^-(1 + a.X^q) ]^1/n . ub +  * ''​Friction Law Maximum Value'' ​           -> <m>C</​m> ​~ max bed slope 
- with a (q-1)^(q-1) q^q and X = ub (C^n N^n As) +  * ''​Friction Law Exponent'' ​      -> m = (n Glen's law) 
-+  ​* ''​Friction Law Linear Velocity'' ​-> <​m>​u_{t0}<​/m>   
-! =Bdrag = C.N.[ X ub^-n / (1 + a.X^q]^1/n + 
 +The effective pressure is defined as <​m>​N ​= -sigma_{nn} ​-p_w</m>, ​ where <​m>​sigma_{nn}</​m>​ is the normal Cauchy stress ​and <​m>​p_w<​/mthe water pressureIf a variable ''​Effective Pressure''​ exists, it is used to evaluate directly <m>N</m>Else, the normal Cauchy stress is estimated from the stress computed at previous timestepThe water pressure is prescribed as an ''​External Pressure'' ​(Negative - Compressive convention, and therefore '​External Pressure'​ should be equal to the opposite of the water pressure in the sif).  
 +       
 + 
  
 ==== SIF contents ==== ==== SIF contents ====
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   Normal-Tangential Velocity = Logical True   Normal-Tangential Velocity = Logical True
   Flow Force BC = Logical True   Flow Force BC = Logical True
 +   
 +  !! Water pressure given through the Stokes '​External Pressure'​ parameter  
 +  !! (Negative = Compressive) 
 +  External Pressure = Equals Water Pressure 
 +   
   Velocity 1 = Real 0.0   Velocity 1 = Real 0.0
   ​   ​
   Slip Coefficient 2 =  Variable Coordinate 1   Slip Coefficient 2 =  Variable Coordinate 1
-    Real Procedure "./​USF_Sliding" "​Friction_Coulomb"​+    Real Procedure "ElmerIceUSF" "​Friction_Coulomb"​
   Slip Coefficient 3 =  Variable Coordinate 1   Slip Coefficient 3 =  Variable Coordinate 1
-    Real Procedure "./​USF_Sliding" "​Friction_Coulomb"​+    Real Procedure "ElmerIceUSF" "​Friction_Coulomb"​
     ​     ​
   !! Parameters needed for the Coulomb Friction Law   !! Parameters needed for the Coulomb Friction Law
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   Friction Law Maximum Value = Real 1.0            !(C=1)   Friction Law Maximum Value = Real 1.0            !(C=1)
   Friction Law PowerLaw Exponent = Real 3.0        !(m = n = 3 Glen's law)    Friction Law PowerLaw Exponent = Real 3.0        !(m = n = 3 Glen's law) 
-  Friction Law Linear Velocity = Real 0.01         !(=1m/a dans un premier temps)+  Friction Law Linear Velocity = Real 0.01         
 End End
 </​code>​ </​code>​
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 ==== Examples ==== ==== Examples ====
-An example ​of the usage of the user function ​//Friction_Weertman// TODO +The Coulomb friction law is tested in ''​[ELMER_TRUNK]/​elmerice/​Tests/​Friction_Coulomb''​ with a direct input of the effective pressure and ''​[ELMER_TRUNK]/elmerice/Tests/Friction_Coulomb_Pw''​ with the effective pressure computed from the stress and a prescribed water pressure.  ​
  
  
userfunctions/coulomb.1352945681.txt.gz · Last modified: 2012/11/15 02:14 by gag
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