Divergence in steady-state FSI problem

[hamed]

Dear Elmer group
I’m working on a steady state FSI problem. But the problem doesn’t converge when I decrease the solid stiffness in order to increase its deflection (convergence doesn’t occur below a distinct value of stiffness). I attached the initial and final configuration of the problem and also the final configuration of the mesh and you can see that the final mesh is ok so I don’t think that the problem stems from the mesh distortion.

I also attached the SIF file.
Thanks for your kind attention, Hamed

Code: Select all

Header
Mesh DB "." "MeshFine"
End

Simulation
Coordinate System = Cartesian 2D
Simulation Type = Steady State
Steady State Max Iterations = 100
Steady State Min Iterations = 2
Output Intervals = 1
Post File = "FSI.ep"
End

! Solid
Body 1
Equation = 1
Material = 1
End

! Air
Body 2
Equation = 2
Material = 2
End

! Solid
Material 1
Density = 2300
Youngs Modulus = 2.0e3   
Poisson Ratio = 0.358
End

! Air
Material 2
Density = 1.2050
Viscosity = 1.983e-5
Poisson Ratio = 0.3
Youngs Modulus = 1.0
End

Solver 1
Equation = Navier-Stokes
Stabilize = True
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Preconditioning = ILU2
Linear System Max Iterations = 1000
Linear System Convergence Tolerance = 1.0e-8
Nonlinear System Max Iterations = 25
Nonlinear System Convergence Tolerance = 1.0e-5
Nonlinear System Newton After Tolerance = 1.0e-50
Nonlinear System Newton After Iterations = 20000
Nonlinear System Relaxation Factor = 1.0
Steady State Convergence Tolerance = 1.0e-4
!Linear System Abort Not Converged = False
End

Solver 2
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 = 0.0 
Nonlinear System Newton After Iterations = 2000000
Nonlinear System Max Iterations = 100
Nonlinear System Convergence Tolerance = 1.0e-5
Nonlinear System Relaxation Factor = 1.0
Steady State Convergence Tolerance = 1.0e-4
!Calculate Velocity = Logical True
End

Solver 3
Equation = Mesh Update
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Preconditioning = ILU2
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-8
Steady State Convergence Tolerance = 1.0e-4
End

Equation 1
Active Solvers = 2
End

Equation 2
Active Solvers(2) = 1 3 
End

! Fluid Inlet
Boundary Condition 1
Target Boundaries = 11
Velocity 1 = 0.01
Velocity 2 = 0.0
Mesh Update 1 = 0.0
End

! Fluid Outlet
Boundary Condition 2
Target Boundaries = 14
Pressure = 0.0
Mesh Update 2 = 0.0
End

! Fluid right symmetry boundary 
Boundary Condition 3
Target Boundaries(2) = 8 13 
Velocity 1 = 0.0
Mesh Update 1 = 0.0
End

! Fluid up fixed boundary 
Boundary Condition 4
Target Boundaries = 10  
Velocity 1 = 0.0
Velocity 2 = 0.0
Mesh Update 2 = 0.0
End

! Fluid left fixed boundary 
Boundary Condition 5
Target Boundaries = 15 
Velocity 1 = 0.0
Velocity 2 = 0.0
Mesh Update 1 = 0.0
End

! FSI 
Boundary Condition 6  
Target Boundaries(2) = 5 4 
FSI BC = True
Mesh Update 1 = Equals Displacement 1
Mesh Update 2 = Equals Displacement 2
Velocity 1 = 0.0
Velocity 2 = 0.0
End

! Solid fixed left wall
Boundary Condition 7
Target Boundaries = 6 
Displacement 1 = 0.0
Displacement 2 = 0.0
End

! Solid symmetry right wall
Boundary Condition 8  
Target Boundaries = 3 
Displacement 1 = 0.0
End

[raback]

Hi Hamed

Elmer offers two strategies

1) Set both "Nonlinear System Max Iterations" to 1 and "Nonlinear System Relaxation Factor" to say 0.5 or even 0.1-0.2 range, if you're desperate. This is the standard relaxation approach. When stiffness goes to zero or the box is fully closed the relaxation factor that works tends to zero.

2) The above will give only limited remedy. For really bad cases of internal FSI there is the method of artificial compressibility. For more details on this see the recent tests (fsi_box and fsi_box2), the relevant sections in Models Manual, and perhaps the FSI papers on the white papers section. The methods have been quite long in Elmer and for suitable problems the kick ass, if you pardon the expression.

-Peter