Divergence problem for steady state compressible flows
I am doing a external flow simulation on a wall. In my meshing , I have a huge aspect ratios (order of 10^5). I have prism layers along the boundary (first layer thickness around 10^7). The unstructured mesh outside the boundary layer has parameters patch conforming,proximity and curvature, min size 10^4, max face size 0.250m and tet size 0.17m . I am using kw sst model, implicit solver, upwind schemes, green gauss node method. The solution is diverging.
I have tried following methods. But they were of no use. 1. Reducing CFL number. Reduced it upto 0.05. 2. Starting with First order scheme and then switching to 2nd order. The residuals get reduced to 10^1 after 30 iterations. But when I switch to Second order upwind scheme, they start diverging again. 3.Reducing relaxation factors. Reduced them to 0.3. 4. Refining. I have refined the grid from 0.05 M nodes to 0.2 M nodes. What else can be done to stop divergence? Also, 1. Is it a good mesh? 2.I wanted to know if meshes with such high aspect ratios will result in divergence ? 3. Is volume mesh adaption a good option for such meshes? I would really appreciate if someone would respond. 
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I have a stopped the simulation when it is diverging and saw the contours. The edge shown here( between inlet and bottom wall) has abnormal values.
Is this the reason for divergence? What could be the problem the mesh or geometry? I would really appreciate anyone's suggestion. 
I have remeshed it and also redrew the geometry.Also, changed the turbulence parameters at the inlet. The residuals are high but constant for sometime and then start to diverge.Also, I am getting these statements after every iteration.
reversed flow in 392 faces on pressureinlet 5. absolute pressure limited to 1.000000e+00 in 9 cells on zone 10009 How can you have reversed flow at the inlet? Any suggestions are welcome. 
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You can probably find posts about this elsewhere on CFDOnline... 
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The inlet and outlet are far apart. My geometry is a windtunnel. Also, can you please see earlier divergence issues I pointed out.

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I have turned on double precision.
My mesh quality Applying quality criteria for tetrahedra/mixed cells. Maximum cell squish = 9.99997e01 Warning: maximum cell squish exceeds 0.99. Maximum cell skewness = 7.60320e01 Maximum aspect ratio = 2.75799e+06 Its empty wind tunnel. The mesh looks like this. It has boundary layers along the wall at the bottom. 
The converging duct starts right up near the inlet... It doesn't matter how far apart the inlet and outlet are, it matters how far the inlet and outlet are from things getting interesting...
I think your inlet is too close to your converging section... 
Also, from your mesh image, I can see that the volume jump between your top prism and the adjacent tetra is huge... The solver probably doesn't like that at all...
You either need more layers so it has time to transition to the larger size... Or you need a smaller tetra size, or you need a larger initial size. Regardless of your Y+ calc, just try out a larger (5 or 10x) initial height and see what happens in the solver. 
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If you need Y+ = 1 , try hexa

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Also, do you think we can have proper mesh if we have complex body in the tunnel later on? I thought unstructured mesh is best for complex geometry. So, is hexa good enough for curved bodies? 
Hexa is good for every problem. In Hexa you can get inflation (aka boundary layer) through edge mesh parameters or more conviently through Ogrid. Thats very simple.

I am confused. How do pictures from post #2 and #5 fit together? Could you please post a picture of your complete domain, with all surfaces described and also what kind of inlets and outlets you have?
One additional thing: Did you check in Fluent, if "General>Scale..." shows the correct size values? 
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But I just wanted to temper Far's comment... on some models (or for some users), hexa is not worth the hassle ;^), which is when tetra/prism or polyhedral meshing kicks in. 
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A lot of the ICEM CFD technology has been exposed... Even ICEM CFD hexa is in ANSYS Meshing as "MultiZone".
But MultiZone is really an automated, almost patch conforming bottom up version of ICEM CFD hexa... Very different from the top down, powerful, flexible tool that ICEM CFD users love, but a great tool in its own right. 
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2) It looks like you use energy equation. What are your boundary conditions? 3) Does your simulation converge without the temperature stuff? 4) So top is also symmetry? How can this curve be symmetric? 5) How can this be "half of" something, when you have 3 of 6 faces with a symmetry boundary condition? Again: Please post an clearly arranged picture of your domain and mark all faces with their meaning. 
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1.Yes, you are right. 2.Yes, I am using energy equation. It started to diverge again. I am using compressible flow. 3. The left is symmetry  half section plane. The other two boundaries are symmetry due to slip condition. 4.Bottom wall is noslip wall and other boundaries are pressure inlet and pressure outlet. 
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