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userfunctions:coulomb [2012/11/15 04:45] gag [SIF contents] |
userfunctions:coulomb [2015/11/26 15:50] gag [Examples] |
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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. |
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==== 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. |
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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). |
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The //Slip Coefficient// in Elmer is then given as\\ | The //Slip Coefficient// in Elmer is then given as\\ |
<m> C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n} </m>\\ | <m> C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n} </m>\\ |
When <m>u_b < u_{t0}</m>, <m>u_b</m> in the previous is replaced by <m>u_{t0}</m>. | When <m>u_b < u_{t0}</m>, <m>u_b</m> in the previous equation is replaced by <m>u_{t0}</m>. |
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The parameters to be given are:\\ | The parameters to be given are:\\ |
* Friction Law Sliding Coefficient -> <m>A_s</m> | * ''Friction Law Sliding Coefficient'' -> <m>A_s</m> |
* Friction Law Post-Peak Exponent -> <m>q >= 1</m> | * ''Friction Law Post-Peak Exponent'' -> <m>q >= 1</m> |
* Friction Law Maximum Value -> <m>C</m> ~ max bed slope | * ''Friction Law Maximum Value'' -> <m>C</m> ~ max bed slope |
* Friction Law Exponent -> m = (n Glen's law) | * ''Friction Law Exponent'' -> m = (n Glen's law) |
* Friction Law Linear Velocity -> <m>u_{t0}</m> | * ''Friction Law Linear Velocity'' -> <m>u_{t0}</m> |
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The effective pressure <m>N = -sigma_{nn} -p_w</m> where <m>sigma_{nn}</m> is the normal Cauchy stress and <m>p_w</m> the water pressure. Here, at time t+dt, the normal Cauchy stress is estimated from the stress computed at time t. The water pressure is prescribed as an //External Pressure// (Positive - Compressive convention). | 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</m> the water pressure. If 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 timestep. The 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). |
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Flow Force BC = Logical True | Flow Force BC = Logical True |
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!! Water pressure given through this parameter (Positive = Compressive) | !! Water pressure given through the Stokes 'External Pressure' parameter |
| !! (Negative = Compressive) |
External Pressure = Equals Water Pressure | External Pressure = Equals Water Pressure |
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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" |
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!! Parameters needed for the Coulomb Friction Law | !! Parameters needed for the Coulomb Friction Law |
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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. |
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