Bumpy convergence in regions of very small y+<0.1

MainzerKaiser · April 4, 2014, 06:35

In a CHT setup, I solve the steady state compressible NS equations with the total energy equation and every scheme set to High Resolution and chose the SST model. The application is a turbine rotor stator cavity with a through flow Re of 2e6 and Mach numbers up to 0.6 in the labyrinth seals.

The CHT evaluation is incorporated in an automatic optimization routine. So for every set of design variables there are the same mesh settings, resulting in y+ values that can vary for every solution from very small numbers to y+=8... So far the high y+ values not necessarily impede my results. I experience problems with very small y+ values below 0.1. The convergence for my fluid residuals get bumpy and the solution takes way to long. Thus, Id rather set my mesh slightly to coarse values for effficient runtimes.

What happens when the y+ values get so small?

JuPa · April 4, 2014, 09:33

I can't talk specifically about your case, but do I do know for some models that too fine a mesh can cause some errors. For example, recently I ran a simulation using the RPI wall boiling model. It didn't like a super fine mesh at the walls (small Y+) and didn't converge well. I did a bit of reading, coarsened the mesh and it worked a treat.

ghorrocks · April 6, 2014, 08:30

It is numerical round-off. As the mesh gets finer the difference between adjacent cells gets smaller. When the difference is small enough that gradients start being affected you will have convergence problems.

The first thing to do is to use double precision numerics. If that does not work then you should carefully coarsen your mesh. Many people on this forum seem scared of y+>1; do a sensitivity check and find out if it is a problem in your case. In many cases y+>1 will work fine, and run much quicker.

MainzerKaiser · April 6, 2014, 08:50

Thanks for the responses.
I already chose the double precision mode before. Could there be another explanation besides round off errors?

A coarsen grid also gave me better results. I just need an explanation why I not generated meshes with y+=1 for every set of design variables.

ghorrocks · April 6, 2014, 17:51

Round off errors is the main cause. Another possibility is that you probably have too fast a transition from the small elements to the large ones, but this is a problem similar to numerical round off as well. Trust me, numerical round off is the key problem. It is normal to have problems converging to extremely fine meshes, especially heavily graded ones (that is, I expect your near wall mesh is much finer than your largest element size).

I have no idea why you did not generate meshes with y+=1 for all design points - you generated the meshes so you have to answer that. And as for the better results on coarsened grid, as I said, as you appear to be hitting numerical round-off limits so coarsening the mesh and moving away from that will help.

April 4, 2014, 06:35	Bumpy convergence in regions of very small y+<0.1	#1
MainzerKaiser Member Join Date: Apr 2011 Posts: 32 Rep Power: 15	In a CHT setup, I solve the steady state compressible NS equations with the total energy equation and every scheme set to High Resolution and chose the SST model. The application is a turbine rotor stator cavity with a through flow Re of 2e6 and Mach numbers up to 0.6 in the labyrinth seals. The CHT evaluation is incorporated in an automatic optimization routine. So for every set of design variables there are the same mesh settings, resulting in y+ values that can vary for every solution from very small numbers to y+=8... So far the high y+ values not necessarily impede my results. I experience problems with very small y+ values below 0.1. The convergence for my fluid residuals get bumpy and the solution takes way to long. Thus, Id rather set my mesh slightly to coarse values for effficient runtimes. What happens when the y+ values get so small?

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April 4, 2014, 09:33		#2
JuPa Senior Member Mr CFD Join Date: Jun 2012 Location: Britain Posts: 361 Rep Power: 14	I can't talk specifically about your case, but do I do know for some models that too fine a mesh can cause some errors. For example, recently I ran a simulation using the RPI wall boiling model. It didn't like a super fine mesh at the walls (small Y+) and didn't converge well. I did a bit of reading, coarsened the mesh and it worked a treat.

April 6, 2014, 08:30		#3
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	It is numerical round-off. As the mesh gets finer the difference between adjacent cells gets smaller. When the difference is small enough that gradients start being affected you will have convergence problems. The first thing to do is to use double precision numerics. If that does not work then you should carefully coarsen your mesh. Many people on this forum seem scared of y+>1; do a sensitivity check and find out if it is a problem in your case. In many cases y+>1 will work fine, and run much quicker.

April 6, 2014, 08:50		#4
MainzerKaiser Member Join Date: Apr 2011 Posts: 32 Rep Power: 15	Thanks for the responses. I already chose the double precision mode before. Could there be another explanation besides round off errors? A coarsen grid also gave me better results. I just need an explanation why I not generated meshes with y+=1 for every set of design variables.

April 6, 2014, 17:51		#5
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	Round off errors is the main cause. Another possibility is that you probably have too fast a transition from the small elements to the large ones, but this is a problem similar to numerical round off as well. Trust me, numerical round off is the key problem. It is normal to have problems converging to extremely fine meshes, especially heavily graded ones (that is, I expect your near wall mesh is much finer than your largest element size). I have no idea why you did not generate meshes with y+=1 for all design points - you generated the meshes so you have to answer that. And as for the better results on coarsened grid, as I said, as you appear to be hitting numerical round-off limits so coarsening the mesh and moving away from that will help.