Divergence of NS solver (patient specific artery)

Numerical methods and mathematical models of Elmer
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shubh_shinde
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Divergence of NS solver (patient specific artery)

Post by shubh_shinde »

Dear all,
I am working on steady state simulations on a patient specific geometry. The non-linear NS solver diverges as soon as simulation is started. The result norm keeps on increasing by iterations and relative change is constant at 2 or 1.999...
However, the solution converges when I increase the viscosity (to 0.01) and decrease the density (to 1) as suggested in tutorials. I have tried using Picard solver, reducing relaxation factor and increasing mesh density but the result is same - solution diverges. The mesh contains hex and prism elements.
I am attaching the sif file and mesh geometry file. I can email the mesh geometry file as I am not able to upload here.

Sincerely,
Shubham
bhaskar.1@iitj.ac.in
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case.sif
sif file
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arterymesh.png
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annier
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Re: Divergence of NS solver (patient specific artery)

Post by annier »

Shubham,
Nice inference.
You can observe at Eq. 2.1 or 2.9 of Elmer Models Manual. The v1,v2,v3 and p are the solutions of N-s equations. And, especially regarding the difficulty in obtaining solutions of velocity due to the convection term (u.\nabla)u , several considerations must be made to make the difference between n and n+1th velocity smaller as possible.
(i) role of density of material - it multiplies the +ve velocity term and solution of convection velocity will be easier for reduced density numerical value.
(ii) role of viscosity of material - it is a part of stress tensor and is subtracted from the +ve velocity terms and the larger it is , the smaller will be the difference in velocity or the magnitude of residuals.
if you are obtaining transient solutions, how about making dt smallers (timestep sizes) as smaller as possible , since it is in the dv/dt ==>> smaller dt would make smaller change in dv. Try more other options as possible , with the sole aim of making v_{n+1} - v_{n} as smaller as possible.
I found it that you are attaching sif file for steady state simulation, so try other options as dt is not involved.

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
shubh_shinde
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Re: Divergence of NS solver (patient specific artery)

Post by shubh_shinde »

Hi Anil,
Thank you for reply.
I understand the roles of density and viscosity in NS equation. I am currently working on steady state simulations. I wonder why the steady state simulation is not converging.
I also tried to implement transient simulation on same geometry as you asked and it resulted in the same result even when the time-step was as small as 0.001. The solver diverges at the start of simulation as soon as the value of density is increased.
Kindly suggest.

Sincerely,
Shubham
annier
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Re: Divergence of NS solver (patient specific artery)

Post by annier »

Shubham,
Try some steps that will influence the iterations induced convergence in the simulations:
1. e.g. direct linear system solver with umfpack method.
2. e.g. iterative linear system solver with Nonlinear System Relaxation Factor < 0.1
Try with some relevant boundary conditions for velocities.
Also find some stabilization techniques.

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
shubh_shinde
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Re: Divergence of NS solver (patient specific artery)

Post by shubh_shinde »

Dear Anil,
Following changes helped me achieve convergence for steady state simulation.
1. Pressure outlet boundary condition over tangential velocities = 0 (it is possible that because of patient specific geometry only normal velocity approximation at the outlet might not be valid)
2. GradP Discretization = True
3. Using GMRES iterative solver over BiCGstab (both are suitable for non-symmetric matrices)

I have also come across Div Discretization in models manual which suggests that this is more stable discretization for high Re. However I have not yet implemented it yet.
Sincerely,
Shubham
annier
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Joined: 27 Aug 2013, 13:51
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Re: Divergence of NS solver (patient specific artery)

Post by annier »

Dear Shubham,
Cheers for the attainment of converged solution, and for future reference, you can attach the codes of solver input file that helped you achieve convergence. Solutions of FEM and N-S equations require a lot of "tricks" for numerical stability and convergence.

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
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