Turek Hron CSM Benchmark Case

FSI_benchmark
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Joined: 20 Jun 2018, 17:48
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Turek Hron CSM Benchmark Case

Dear Elmer Users
I am quite new in FEM and CSM calcualtion. At the moment I am trying to get the CSM1 case results proposed by the Turek and Hron Paper: http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf.
The problem is quite simple: a beam is fixed on one side. The body gets a volume force. My values are not converging to the reference data. I calculate the case on an equidistant hexahedral mesh. Here are my results so far:

CSM1 Test CASE Turek Hron
Grid 70 x 4 x 4
displacement in x: -5.6069263e-13 m
displacement in y: -0.07580281 m

Grid 140 x 8 x 8
displacement in x: -3.7717619e-14 m
displacement in y: -0.078753294 m

Grid 280 x 16 x 16
displacement in x: -2.6036727e-14, m
displacement in y: -0.079596393 m

Turek Hron Ref Data
displacement in x: −0.007187 m
displacement in y: -0.06610 m

I am happy for any hints and ideas that you have. I don't know why I get this deviation, especially for the displacement for the x diretion. Thank you a lot!

-------------------------------------------
My Case File:
CHECK KEYWORDS Warn
Mesh DB "."
Include Path ""
Results Directory ""
End

Simulation
Max Output Level = 5
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Solver Input File = case.sif
Post File = case.vtu
End

Constants
Gravity(4) = 0 -1 0 0
Stefan Boltzmann = 5.67e-08
Permittivity of Vacuum = 8.8542e-12
Boltzmann Constant = 1.3807e-23
Unit Charge = 1.602e-19
End

Body 1
Target Bodies(1) = 1
Name = "Body 1"
Equation = 1
Material = 1
Body Force = 1
End

Material 1
Name = "Rubber"
Density = 1000.0
Poisson ratio = 0.4
Youngs modulus = 1.4e6
End

Equation 1
Name = "Equation 1"
Calculate Stresses = True
Active Solvers(1) = 1
End

Solver 1
Equation = Nonlinear elasticity
Procedure = "StressSolve" "StressSolver"
Variable = -dofs 3 Displacement
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 1
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Iterative
Linear System Iterative Method = GCR
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-8
Linear System Preconditioning = ILU1
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = False
Linear System Residual Output = 1
Linear System Precondition Recompute = 1
End

Solver 2
Exec Solver = after timestep
Equation = "result output"
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output File Name = "beam"
Output Format = String "vtu"
Binary Output = False
Save Geometry Ids = True
Ascii Output = True
End

Boundary Condition 1
Target Boundaries(1) = 5
Name = BoundaryCondition 1
Displacement 1 = 0
Displacement 2 = 0
Displacement 3 = 0
End

Body Force 1
Name = "Gravity"
Stress Bodyforce 2 = \$ -2.0*1000
End
---------------------------------------------------------------

raback
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Joined: 22 Aug 2009, 11:57
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Location: Espoo, Finland
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Re: Turek Hron CSM Benchmark Case

Hi FSI

You seem to solving in 3D? The original case is in 2D if I'm mistaken. Does it assumes plane stress or plane strain? Oftentimes it is a good idea to use quadratic elements for elasticity since they give better precision for the same computational cost.

This is a very nice case. However, I believe that these very competent experts made the case such that it would prove their monolithic approach would be needed. Are you really solving such cases where the coupling is so strongly? We have successfully used Elmer to model blood flow simulations which are also known to be tricky. There we have a nice remedy in the artificial compressibility that mimics the elastic response of the artery. Even that strategy faces here some challenges as the elasticity problem has more inertial effects and the pressure-volume response cannot easily be used to improve the convergence.

-Peter

FSI_benchmark
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Joined: 20 Jun 2018, 17:48
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Re: Turek Hron CSM Benchmark Case

Dear Peter,
thank you a lot for your quick response! What do you mean by plane stress or plane strain. As far as I understand displacement is calculated before the stress solver is taken into account. At the moment I am not care about coupling approaches I have different schmemes in mind, but this is another topic. My focus is to benchmark the CSM solver and before I don't get the same vaules as in the paper for the CSM case, I can't expect correct values in my FSI.
I followed your hint and run the case again in 2D with a quad mesh.
The results are now for a grid of 580 x 32
displacement in x: -7.6934897e-15 m
displacement in y: -0.067089553 m

Now I have two questions:
Why I get a deviation from the 3d to the 2d case in the y displacement (How affect the 3rd degree of freedom for the displacement calculation the result?). The y displacement seems now correct in comparison to the ref data.
Why I don't get a displacement in x direction? It seems to converging against zero both 2d and 3d.

Best Marc

raback
Posts: 3366
Joined: 22 Aug 2009, 11:57
Antispam: Yes
Location: Espoo, Finland
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Re: Turek Hron CSM Benchmark Case

Hi Marc,

You might rather use the geometric nonlinear module: ElasticSolve.

By the way, the default solver settings for elasticity solver are often quite slow. If you compute something larger you may want to touch them also.

-Peter

FSI_benchmark
Posts: 3
Joined: 20 Jun 2018, 17:48
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Re: Turek Hron CSM Benchmark Case

Hi Peter,

thank you again for your hint. Now I get quite nice values for the displacement (error < 1% to the reference values). Is their any literature or an extended Solver Manual, where I can get all of this informations?

Best Marc

raback