! 2D arterial flow simulation where inlet is enforced with a physical
! pump and outlet is obtained from a 1D lumped model utilizing the method
! of characteristics.
!
! This test case is derived from the older tutorial case
! "Blood ejection from a ventricle into aorta".
! Here the 1D mesh is created internally while in the old
! tutorial case it was done by modifying the mesh files directly.
!
! References for the methods used:
!
! 1) A method for partitioned fluid-structure interaction computation of flow in arteries
! Medical Engineering & Physics, Volume 30, Issue 7, September 2008, Pages 917-923
! Esko Jarvinen, Peter Raback, Mikko Lyly, Juha-Pekka Salenius
!
! 2) Fluid-structure interaction boundary condition by artificial compressibility
! CFD Eccomas 2001, Swansea
! Peter Raback, Juha Ruokolainen, Mikko Lyly, and Esko Jarvinen
!
! 13.8.2013 / P.R. - case included as test
! 27.1.2020 / P.R. - minor modification to simplify geometry
Check Keywords Warn
Header
Mesh DB "." "contra"
End
Constants
Gravity(4) = Real 0 -1 0 9.81
Stefan Boltzmann = Real 5.67e-8
End
Simulation
Coordinate System = Axi Symmetric
Simulation Type =Transient
Steady State Max Iterations = 250
TimeStepping Method = BDF
BDF Order = 2
Timestep Sizes = 0.001
TimeStep Intervals = 2 !300
Output Intervals = 1
Max Output Level = 5
Simulation Timing = Logical True
End
Body 1
Equation = 1
Material = 1
End
Body 2
Equation = 1
Material = 1
End
Body 3
Equation = 1
Material = 2
End
Body 4
Equation = 2
Material = 3
End
Body 5
Equation = 3
Material = 4
Body Force = 1
Initial Condition = 1
End
Initial Condition 1
Wnodal = Variable Coordinate
Real Procedure "ArteryOutlet" "OutletInit"
End
Body Force 1
Source = Real 0.0
End
Material 1
Name = "Blood"
Density = 1000.0
Viscosity = 3.5e-3
Mesh Youngs Modulus = 1.0
Mesh Poisson Ratio = 0.3
End
Material 2
Name = "Blood with FSI"
Density = 1000.0
Viscosity = 3.5e-3
Mesh Youngs Modulus = 1.0
Mesh Poisson Ratio = 0.3
Compressibility Model = Artificial Compressible
Artificial Compressibility = 2.4E-5
End
Material 3
Name = "Elastic Wall"
Density = 1010.0
Youngs Modulus = 3.0e5
Poisson Ratio = 0.45
End
Material 4
Name = "1D Artery"
Density = 1010.0
Artery Wall Youngs Modulus = Real 3.0e5
Artery Radius = Real 0.0135
Artery Wall Thickness = Real 0.002
Artery Poisson Ratio = Real 0.45
End
Solver 1
Equation = Artery Outlet Solver
Time Derivative Order = 1
Variable = Wnodal
Procedure = "ArteryOutlet" "OutletCompute"
Linear System Solver = Direct
Linear System Direct Method = Banded
Nonlinear System Max Iterations = Integer 1000
Nonlinear System Convergence Tolerance = Real 1.0e-8
Optimize Bandwidth = False
! These define the 1D mesh that is created on-the-fly for this solver
1D Mesh Create = Logical True
1D Element Order = Integer 1
1D Number Of Elements = Integer 20
1D Mesh Length = Real 0.1
1D Active Direction = Integer 2
1D Body Id = Integer 5
End
$Relax = 1.0
Solver 2
Equation = Navier-Stokes
Stabilize = Logical True
Linear System Solver = Direct
Linear System Direct Method = umfpack
Nonlinear System Max Iterations = 1
Nonlinear System Convergence Tolerance = 1.0e-3
Nonlinear System Newton After Tolerance = 5.0e-2
Nonlinear System Newton After Iterations = 0
Steady State Convergence Tolerance = 1.0e-4
Nonlinear System Relaxation Factor = $Relax
Calculate Viscous Force = Logical True
End
Solver 3
Equation = Elasticity Solver
Variable = Displacement
Variable DOFs = 2
Procedure = "ElasticSolve" "ElasticSolver"
Linear System Solver = Direct
Linear System Direct Method = umfpack
Nonlinear System Newton After Tolerance = 5.0e-2
Nonlinear System Newton After Iterations = 0
Nonlinear System Max Iterations = 1
Nonlinear System Convergence Tolerance = 1.0e-4
Steady State Convergence Tolerance = 1.0e-4
Nonlinear System Relaxation Factor = $Relax
End
Solver 4
Equation = Mesh Update
Linear System Solver = Direct
Linear System Direct Method = umfpack
Linear System Symmetric = True
Steady State Convergence Tolerance = 1.0e-4
End
Solver 5
Equation = SaveScalars
Procedure = "SaveData" "SaveScalars"
Exec Solver = never ! After timestep
Filename = f.dat
Variable 1 = coupled iter
End
Solver 6
Equation = "ResultOutput"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = case
Vtu format = Logical True
Save Geometry IDs = True
! Suppress saving of lines
Minimum Mesh Dimension = Integer 2
End
Equation 1
Navier-Stokes = True
Mesh Update = True
End
Equation 2
Elasticity Solver = Logical True
End
Equation 3
Artery Outlet Solver = Logical True
End
! Inlet where motion is defined
Boundary Condition 1
Name = "PumpingBC"
Target Boundaries(1) = 1
Velocity 1 = 0
Velocity 2 = Equals Mesh Velocity 2
Mesh Update 1 = 0.0
Mesh Update 2 = Variable Time
Real Procedure "./Motion" "Motion"
End
! Outlet coupled weakly to the characteristic solver 1)
! using special user-defined routine.
Boundary Condition 2
Name = "OutletBC"
Target Boundaries(1) = 2
Flux Integrate = Logical True
Flow Force BC = True
Pressure 2 = Variable Time
Real Procedure "ArteryOutlet" "OutletPres"
Mesh Update 2 = Real 0
! This tag needed for coupled.
1D Fluid Coupling = Logical True
End
! Conditions at the r=0 axis.
Boundary Condition 3
Name = "SymmetryBC"
Target Boundaries(1) = 3
Velocity 1 = 0
Mesh Update 1 = Real 0
End
! Start of artery wall.
Boundary Condition 4
Name = "StructureStart"
Target Boundaries(1) = 4
Displacement 1 = 0.0
Displacement 2 = 0.0
End
! End of artery wall.
Boundary Condition 5
Name = "StructureEnd"
Target Boundaries(1) = 5
Displacement 1 = Variable Time
Real Procedure "ArteryOutlet" "OutletdX"
Displacement 2 = 0.0
1D Structure Coupling = Logical True
End
! Fluid-structure interaction BCs.
Boundary Condition 6
Name = "FSI"
Target Boundaries(1) = 6
Velocity 1 = Equals "Mesh Velocity 1"
Velocity 2 = Equals "Mesh Velocity 2"
Mesh Update 1 = Equals "Displacement 1"
Mesh Update 2 = Equals "Displacement 2"
FSI BC = Logical True
End
! Fluid wall starying fixed
Boundary Condition 7
Name = "FluidWall"
Target Boundaries(1) = 7
Mesh Update 1 = Real 0.0
Mesh Update 2 = Real 0.0
Velocity 1 = 0.0
Velocity 2 = 0.0
End
! Fluid wall stretching with the pumping motion
Boundary Condition 8
Name = "StretchingWall"
Target Boundaries(1) = 8
Mesh Update 1 = Real 0.0
Velocity 1 = 0.0
Velocity 2 = 0.0
End
Solver 2 :: Reference Norm = 4.32436552E-03
Solver 3 :: Reference Norm = 1.55732880E-06
Solver 4 :: Reference Norm = 1.33737099E-06
