~~NOTOC~~
===== Fabric Evolution - DG Fabric Solver =====
==== General Informations ====
* **Solver Fortran File:** ''FabricSolve.f90''
* **Solver Name:** ''FabricSolver''
* **Required Output Variable(s):** ''Fabric''
* **Required Input Variable(s):** ''Temperature'', ''AIFlow'',
* **Optional Output Variable(s):** ''EigenV''
* **Optional Input Variable(s):** ''Mesh Velocity''
==== General Description ====
This solver solves the fabric evolution equations for the anisotropic law obtained from the [[solvers:aiflow|AIFlow solver]]. In Elmer/Ice, the fabric is described using the 5 independent components of the second-order orientation tensor. The grain rotation is induced by the macroscopic strain-rate and the deviatoric stress, and their relative influence is controlled by the ''interaction parameter'' (from 0 for purely strain-induced rotation to 1 for purely stress induced rotation). To account for other phenomena than grain rotation, one can use the ''diffusion parameter''.
The eigenvalues of the second-order orientation tensor ''Fabric'' are computed if the variable ''EigenV'' exists.
==== SIF contents ====
! Solve the equation for the orthotropic flow law
! AIFlow Solvers
Solver 1
Equation = AIFlow
Variable = AIFlow
Variable DOFs = 4 !3 for 2D (u,v,p) -- 4 for 3D (u,v,w,p)
Exported Variable 1 = Temperature ! Define Temperature Mandatory!
Exported Variable 1 DOFS = Integer 1
Exported Variable 2 = Fabric ! Define Fabric Variable
Exported Variable 2 DOFS = Integer 5 ! Mandatory if Isotropic=False
! If non-linearity introduced using deviatoric stress second invariant
Procedure = "ElmerIceSolvers" "AIFlowSolver_nlS2"
End
! Fabric solver itself
Solver 2
Equation = Fabric
Variable = -nooutput Compfab ! dumy variable
Variable DOFs = 1 !FabricSolver compute each variable independently,
!Picard Type iterations
Procedure = "ElmerIceSolvers" "FabricSolver"
Discontinuous Galerkin = Logical True
End
! Material
Material 1
!!!! For Fabric Solver
Interaction Parameter = Real 0. ! 0 => Fabric Evolution function of Strain-rates
! 1 => Fabric Evolution function of dev stresses
!If not defined set to the default value given in the Viscosity File
Diffusion Parameter = Real 0. ! Diffusion term. By default set to 0 if not defined
End
!Initial Conditions
Initial Condition 1
! Define an isotropic fabric
Fabric 1 = Real 0.33333333333333 !a2_11
Fabric 2 = Real 0.33333333333333 !a2_22
Fabric 3 = Real 0. !a2_12
Fabric 4 = Real 0. !a2_23
Fabric 5 = Real 0. !a2_13
...
End
! Boundary Conditions
Boundary Condition 1
Target Boundaries = 1
! Dirichlet conditions for Fabric
! only if inflow boundary condition, no condition for outflow
Fabric 1 = Real 0.33333333333333 !a2_11
Fabric 2 = Real 0.33333333333333 !a2_22
Fabric 3 = Real 0. !a2_12
Fabric 4 = Real 0. !a2_23
Fabric 5 = Real 0. !a2_13
End
==== Examples ====
Download an example using the ''Fabric'' Solver. TODO
==== References ====
* Fabric evolution and numerical implementation within Elmer/Ice are presented in this publication:\\
Gillet-Chaulet F., O. Gagliardini , J. Meyssonnier, T. Zwinger and J. Ruokolainen, 2006. Flow-induced anisotropy in polar ice and related ice-sheet flow modelling. J. Non-Newtonian Fluid Mech., 134, p. 33-43.