AIFlow

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Name of the package: AIFlow_source.tar.gz
Latest Updated: 2009/05/07
Names of source code files: AIFlowSolve_nlD2.f90, AIFlowSolve_nlS2.f90, Fabric.f90, FabricSolve.f90, 040010010.Va
Name(s) of contained subroutine(s): AIFlowSolver, FabricSolver

Description of AIFlowSolve_nl{S,D}2
Solves the equation for the orthotropic flow law. There are two different versions depending on the non-linear extension of the flow law applied (see SIF section comments).

Description of FabricSolver
Solves the fabric evolution using a Discontinuous Galerkin (DG) method.

Description of the file 040010010.Va
Contains the dimensionless viscosity tabulated on a regular grid in the space spanned by the two largest eigenvectors of the 2nd order orientation tensor. This file is output of the result from a previously separately run micro-macro model (Fabric.f90). Nomenclature of the file:
abcdefghi.Ma
grain anisotropy parameter beta=0.abcd
grain anisotropy parameter=> gamma=e.fg
stress exponent n=h.i
model used for tabulation =M (V holds for VPSC model)

N.B.: The attached micro-macro (Fabric.f90) model does not work for general 3D deformation, but only for cases where one of the eigenvectors is aligned with the reference frame vector. That is due to the fact that the complete 3D version relies on licensed code that is not compatible with free distribution.

Keywords of AIFlowSolve

! Solve the equation for the orthotropic flow law
! and the fabric evolution
!
!  see Gillet-Chaulet et al., Journal of Non-Newtonian Fluid Mechanic, 134, (2006), pp 33-43 for details.
!  contact: GILLET-CHAULET Fabien (fall[at]bas[dot]ac[dot]uk)
!           and/or
!           GAGLIARDINI Olivier (gagliar[at]lgge[dot]obs[dot]ujf-grenoble[dot]fr
!!!!!AIFlow Solvers
Solver 1
  Equation = AIFlow
  Variable = AIFlow
  Variable DOFs = 3                        !3 for 2D -- 4 for 3D


  Exported Variable 1 = Temperature        !Define Temperature Mandatory!!
  Exported Variable 1 DOFS = Integer 1

  Exported Variable 2 = Fabric             !Define Fabric Variable !!Mandatory if Isotropic=False
  Exported Variable 2 DOFS = Integer 5

  Exported Variable 3 =  StrainRate        ! Compute SR
  Exported Variable 3 DOFS = Integer 4     !4 in 2D  6 in 3D (11,22,33,12,23,31)

  Exported Variable 4 =  DeviatoricStress  ! Compute Stresses
  Exported Variable 4 DOFS = Integer 4     !4 in 2D  6 in 3D  (11,22,33,12,23,31)

  Exported Variable 4 =  Spin              ! Compute Spin
  Exported Variable 4 DOFS = Integer 1     !1 in 2D  3 in 3D (12,23,31)


  Procedure = "path/to/Exec/Solver/AIFlowSolve_nlS2 or AIFlowSolve_nlD2" "AIFlowSolver"
End</pre>
'''Keywords for FabricSolver'''
<pre>!!!!!Fabric Solver
Solver 2
  Equation = Fabric
  Variable = -nooutput Compfab    ! dumy variable
  Variable DOFs = 1               !FabricSolver compute each variable independently, Picard Type iterations

  Procedure = "/path/to/FabricSolver/" "FabricSolver"
  Discontinuous Galerkin = Logical True

End

Keywords in other sections

!!!!!!!!!!!!!!!!!!!!!!!! Body Force
Body Force 1
  AIFlow Force 2 = Real -0.00899  ! body force, i.e. gravity * density
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Material
Material 1

!!!!! For AIFlows...
  Powerlaw Exponent = Real 3.0         ! sqrt(tr(S^2/2))^n if AIFlow_nlS2 sqrt(tr(2D^2))^(1/n-1) if  AIFlow_nlD2
  Min Second Invariant = Real 1.0e-10  ! Min value for the second invariant of strain-rates
  Reference Temperature = Real -10.0   ! T0 (Celsius)!
  Fluidity Parameter = Real 20.        ! Bn(T0)
  Limit Temperature = Real -5.0        ! TL  (Celsius)!
  Activation Energy 1 = Real 7.8e04    ! Joule/mol for T<TL
  Activation Energy 2 = Real 7.8e04    ! Joule/mol for T>TL

  Viscosity File = FILE "040010010.Va"

  Isotropic = Logical False !If set to true Glen flow law (no need to defined Fabric)

!!!! 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 Viscosity File
  Diffusion Parameter = Real 0.   ! Diffusion term. By default set to 0 if not defined
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Initial Conditions
Initial Condition 1

  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

  AIFlow 1 = Real 0.0              ! u_1
  AIFlow 2 = Real 0.0              ! u_2
  AIFlow 3 = Real 0.0              ! p for 2D u_3 for 3D
  AIFlow 4 = Real 0.0              ! only for 3D = p
End

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! BC
Boundary Condition 1
  Target Boundaries = 1


!dirichlet condition for velocity
   AIFlow 1 = Real0.
   AIFlow 2 = Real0.

!dirichlet condition 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


Boundary Condition 2
  Target Boundaries = 2
! Neuman condition for AIFlow
  Normal force = Real 0.   ! force along normal
  Force 1 = Real 0.        ! force along x
  Force 2 = Real 0.        ! force along y
  Force 3 = Real 0.        ! force along z

  AIFlow Slip Coeff 1 = Real 0.   ! Slip coeff.

End