# Mesh Instability

Hello, I am trying to do natural convection via Fluent but I have a really strange problem with meshing. My setup is simple I have 2D geometry and it has 4 walls which left and right wall are adiabatic and top wall is cold wall and bottom wall is hot wall, my temperature difference 10 (303K-293K).My mesh is triangular and it is really good and symmetrical. My Rayleigh number is 10^5.

My problem is that if I have 12464 element numbers there is no problem it is converged but if I have 12312 element numbers there is oscillation in my residual like in the picture and my Nusselt numbers decrease about 50% from its real value. So you can say 12464 element numbers are good what you want. I have tried many combinations and I found 12464 element numbers with luck so if I set little small element size I had 12925 element size and there will not give great residual and it will has oscillation. Now, I have to do some little change in my geometry for aspect ratio but this is a really small changing like just 1 mm increasing the length of opposite walls. So now I did a lot of things for meshing but unfortunately, still there is oscillation in my residual.

I am tried with default Coupled method because in the other methods I can see my Nusselt number decreasing but residuals do not have visible things to understand that some things wrong. So I am solving with Coupled method because I can observe there is a problem or not.

Residual oscilation:

My mesh:

You can see my mesh and you can sure I tried many things like refinement, set about 200.000 element numbers, set about 700 element numbers, quadrilaterals and more. I want to say another strange thing that when mesh has 200.000 element numbers my Nusselt number is about 2.50 and if I have 700 element numbers my Nusselt number is about 2.50 so the deviation is about zero. Fluent like obsessed some point and decreases every time that point I can't understand what is problem.

I hope there is a solution for this problem.

Best Regards,

Alp

## Comments

Natural convection tends to be slightly unstable, so it's normal to have some noise on the residuals. Since all the heat comes from the walls, what is the difference in y+ between the meshes? What happens if you further refine the mesh?

I'm sorry for the late reply. I am new in ANSYS. I analyzed a laminar case so I looked at contour settings for y+ but I didn't find it.

I want to say another something that I realized. Actually, there is a problem with the specific Rayleigh Number which is Ra=10^5. As you can see in the picture mean Nu number of 10^5 looks really strange. When I look at the residual for Ra=10^5, the mean Nu is almost 3.20 in 30 iterations and I expect like that Nu number ends up but then there is a dramatic falling at 2.50 and go constant. Why there is a problem like this I don't know. The mesh is same in all Rayleigh numbers in the picture. There is no problem with other Rayleigh numbers like falling suddenly.