[mkhm]

Dear foamers,



I am running rhoCentralFoam for supersonic cases. The case is 2D, inviscid and different cases with different mach numbers ranging from 3 to 8 have been considered. I have 3e+6 of cells. What I do is first to consider very coarse mesh (10000) and map fields to a much refined mesh of 3e+6 cells. It takes 10 to 14 days to have convergence. I run refined mesh in parallel with 64 to 128 processors and I reach acceptable convergence. However, my supervisor says that it should not take too much time and within half days, I should have the convergence. Now, I should say that I am really desperate and I do not know where is the problem. The mesh ? the setting in fvSchemes, the setting in the fvSolution ? But, the only thing that can help me is the experience of you the foamers. Do you really manage to have convergence with 3e+6 cells in a supersonic case running the rhoCentralFoam within few hours ?

[usv001]

Hi Mary,

As you know, rhoCentralFoam is a transient solver. So, it's not exactly designed for achieving fast convergence for steady-state problems. You'll need an implicit solver with some dual time-stepping for steady-state problems. Check out Ref. [1] where they compare an implicit solver and rhoCentralFoam. You'll notice that rhoCentralFoam does not have very good convergence compared to the implicit solver. If it does converge, it'll probably take longer. How much longer, depends on the case.

Another problem could be with TVD schemes used for pose/neg sided reconstructions themselves. I recall facing convergence issues with these schemes. So, I switched to using the Venkatakrishnan limiter (refer to Ref. [2]) which is supposed to be better. According to you, the solution does converge although it takes a long time to do so. So, I am not sure if this will make a big difference.

What you could try to do is a kind of 'multi-grid' method similar to what you're already doing now. Create a series of meshes with increased refinement. Start simulating on the coarsest mesh. When solution converges, map the fields to next mesh and run it till convergence. Do this until you reach the most refined mesh. Hopefully, this will take a shorter time but whether it'll take half-a-day is hard to say.

References
[1] C. Shen, X.-L. Xia, Y.-Z. Wang, F. Yu, and Z.-W. Jiao, Implementation of density-based implicit LU-SGS solver in the framework of OpenFOAM, Adv. Eng. Softw. 91, (2016)
[2] V. Venkatakrishnan, Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J. Comput. Phys. 118, 1 (1995)

Cheers,
USV

Note: I am by no means an expert in the area of implicit solvers or multi-grid methods. So, please correct me if I am wrong about anything.

[mkhm]

Originally Posted by usv001

Hi Mary,

As you know, rhoCentralFoam is a transient solver. So, it's not exactly designed for achieving fast convergence for steady-state problems. You'll need an implicit solver with some dual time-stepping for steady-state problems. Check out Ref. [1] where they compare an implicit solver and rhoCentralFoam. You'll notice that rhoCentralFoam does not have very good convergence compared to the implicit solver. If it does converge, it'll probably take longer. How much longer, depends on the case.

Another problem could be with TVD schemes used for pose/neg sided reconstructions themselves. I recall facing convergence issues with these schemes. So, I switched to using the Venkatakrishnan limiter (refer to Ref. [2]) which is supposed to be better. According to you, the solution does converge although it takes a long time to do so. So, I am not sure if this will make a big difference.

What you could try to do is a kind of 'multi-grid' method similar to what you're already doing now. Create a series of meshes with increased refinement. Start simulating on the coarsest mesh. When solution converges, map the fields to next mesh and run it till convergence. Do this until you reach the most refined mesh. Hopefully, this will take a shorter time but whether it'll take half-a-day is hard to say.

References
[1] C. Shen, X.-L. Xia, Y.-Z. Wang, F. Yu, and Z.-W. Jiao, Implementation of density-based implicit LU-SGS solver in the framework of OpenFOAM, Adv. Eng. Softw. 91, (2016)
[2] V. Venkatakrishnan, Convergence to steady state solutions of the Euler equations on unstructured grids with limiters, J. Comput. Phys. 118, 1 (1995)

Cheers,
USV

Note: I am by no means an expert in the area of implicit solvers or multi-grid methods. So, please correct me if I am wrong about anything.

Thanks a lot for your answer. I'll read carefully the papers that you mentioned. By the way, do you know any other solvers from openfoam able to capture shocks and suitable to be used for the simulation of supersonic cases ?


Best regards,

Mary

[mkhm]

I am wondering if the design of the geometry is such that the shocks are avoided, is there any real need to use rhoCentralFoam ? Is there any other solver suitable for numerical simulation of a transonic nozzles being implicit ?



Best regards,

Mary