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! Solve for an analytical solution of the dating equation !
! dA/dt + u.grad(A) = 1 !
! In 1D + steady !
! u dA/dx = 1 => solution of the form A = ln(K v) with u = v/v' !
! !
! v = L^2 + x^2 => u = (L^2 + x^2)/(2x) and A = ln((L^2+x^2)/(L^2+1)) !
! Exx = 1/2*(1-(L/x)^2) !
! !
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Check Keywords Warn
Header
Mesh DB "." "mesh"
End
$L = 100.0
$ function Aana(x) \
import L {\
_Aana = ln((L^2+x^2)/(L^2+1.0)) ;\
}
$ function Exx(x) \
import L {\
_Exx = 0.5*(1.0-(L/x)^2) ;\
}
$ function ux(x) \
import L {\
_ux = (L^2+x^2)/(2.0*x) ;\
}
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Simulation
Coordinate System = Cartesian 2D
Simulation Type = Steady State
Steady State Max Iterations = 1
Steady State Min Iterations = 1
Output Intervals = 10
Post File = "age.vtu"
max output level = 4
End
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Body 1
Equation = 1
Material = 1
Body Force = 1
Initial Condition = 1
End
Body Force 1
DGAge Source = Real 1.0
End
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Material 1
! minimum age is zero but should not be needed
DGAge Lower Limit = Real 0.0
!Reaction rate is equal to -tr(Eij) for compressible fluid
DGAge Gamma = Variable Coordinate 1
Real MATC "-Exx(tx)"
End
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Initial Condition 1
DGAge = REal 0.0
Age = Real 0.0
Porous 1 = Variable Coordinate 1
Real MATC "ux(tx)"
Porous 2 = Real 0.0
Porous 3 = Real 0.0
AgeAna = Variable Coordinate 1
Real MATC "Aana(tx)"
Exx = Variable Coordinate 1
Real MATC "Exx(tx)"
End
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Solver 1
Exec solver = Never
Equation = String "PorousFlow"
Procedure = "ElmerIceSolvers" "PorousSolver"
Variable = "Porous"
Variable DOFs = 3
Exported Variable 1 = AgeAna
Exported Variable 1 DOFs = 1
Exported Variable 2 = Exx
Exported Variable 2 DOFs = 1
Optimize Bandwidth = False
! Use p elements
Stablization Method = String pBubbles
Linear System Solver = "Direct"
Nonlinear System Convergence Tolerance = 1.0E-05
Nonlinear System Max Iterations = 50
End
Solver 2
Equation = "AdvReact"
Exec Solver = "After Timestep"
Procedure = File "AdvectionReaction" "AdvectionReactionSolver"
! this is the DG variable, which is not part of the output
Variable = -nooutput "DGAge"
! this tells that the solver is run on DG mesh
Discontinuous Galerkin = Logical True
! the solver can account for upper and lower limits of the variable
! imposed by formulation of an variational inequality (VI)
! next line switches the VI to be accounted for
Limit Solution = Logical True
Linear System Solver = Direct
! Variational inequality makes it a non-linear problem
Nonlinear System Max Iterations = 40
Nonlinear System Min Iterations = 20
Nonlinear System Convergence Tolerance = 1.0e-06
! This is the variable that is used to interpolate
! the DG solution to the regular FEM mesh in order
! to get a correct output
Exported Variable 1 = Age
Exported Variable 1 DOFS = 1
End
!Solver 3
! Exec Solver = After All
! Procedure = File "SaveData" "SaveLine"
! Filename = "results.dat"
! File Append = Logical False
!End
Solver 3
Exec Solver = After All
Equation = SaveScalars
Procedure = File "SaveData" "SaveScalars"
Filename = "results.dat"
Variable 1 = String "Time"
Variable 2 = String "Age"
Operator 2 = String "max"
Variable 3 = String "Age"
Operator 3 = String "min"
!Variable for comparison
!Variable 2 = String "AgeAna"
!Operator 2 = String "max"
!Variable 3 = String "AgeAna"
!Operator 3 = String "min"
End
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Equation 1
Active Solvers(3) = Integer 1 2 3
Flow Solution Name = String "Porous"
Convection = Computed
End
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Boundary Condition 1
Target Boundaries = 4
DGAge = Real 0.0
End
Boundary Condition 2
Target Boundaries = 1
Save Line = Logical True
End
Solver 2 :: Reference Norm = Real 0.34220875
Solver 2 :: Reference Norm Tolerance = Real 1E-06
