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===== User Function USF_ShapeFactor =====

==== General Informations ====
  * **USF Fortran File:** ''USF_ShapeFactor.f90''
  * **USF Name:** ''LateralFriction_x'' and ''LateralFriction_y'' 
  * **Required Input Variable(s):** None


==== General Description ====
This user function return the modified gravity force -**g** +(1-f)(**g**.**t**).**t** \\
where **t** is the tangent vector to the upper surface and f the shape factor.
The shape factor f can be given or calculated as a function of h(x,t) for rectangular or parabola valley shapes.

This solver works only in 2D (no sense in 3D). It works for non-structured mesh.


==== SIF contents ====
Here are the three options to use the ''USF_ShapeFactor'' user function. 
In the first option, the shape factor f is simply given as a parameter ''Shape Factor'':
<code>
Body Force 1
  Flow BodyForce 1 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_x"
  Flow BodyForce 2 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_y"
  Shape Gravity 1 = Real  0.0                                 
  Shape Gravity 2 = Real -9.7696e15       

  Shape Factor = real $shapefactor
End
</code>

In the second option, the shape factor f is computed for a rectangular valley of given width:
<code>
Body Force 1
  Flow BodyForce 1 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_x"
  Flow BodyForce 2 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_y"
  Shape Gravity 1 = Real  0.0                                 
  Shape Gravity 2 = Real -9.7696e15       

  Rectangle Shape = Logical True
  Rectangle Width = Real 2.0e3
End
</code>

In the third option, the shape factor f is computed for the parabola type transverse valley  y = b + a*z^2, where a is given by the ''Parabola afactor'' keyword and b is the bedrock elevation of the central line:
<code>
Body Force 1
  Flow BodyForce 1 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_x"
  Flow BodyForce 2 = Variable Coordinate 1
     Real Procedure "ElmerIceUSF" "ShapeFactorGravity_y"
  Shape Gravity 1 = Real  0.0                                 
  Shape Gravity 2 = Real -9.7696e15       
  
  Parabola Shape = Logical True
  Parabola afactor = Real 0.0005
End
</code>


In all cases, the two keywords //Shape Bedrock// and //Shape Surface// are used to locate nodes belonging on the bedrock and surface boundaries, respectively.

<code>
! Bedrock
Boundary Condition 1
  Target Boundaries = 1
  ...
  Shape Bedrock = Logical True
End

! Upper Surface
Boundary Condition 3
  Target Boundaries = 3
  ...
  Shape Surface = Logical True
End
</code>

==== Examples ====
An example using the user function ''USF_ShapeFactor'' can be found in ''[ELMER_TRUNK]/elmerice/Tests/ShapeFactor''.

==== Reference ====
When used this solver can be cited using the following references:\\
Jay-Allemand M., F. Gillet-Chaulet, O. Gagliardini and M. Nodet, 2011. Investigating changes in basal conditions of Variegated Glacier prior to and during its 1982–1983 surge. The Cryosphere, 5, p. 659-672, doi:10.5194/tc-5-659-2011.