Fluent diverges when using inflation layers
 

I'm simulating a 2D wedge in a flow with the transient standard k-epsilon model. The Reynolds number is around 400000.
The geometry is shown below.

The mesh without inflation layers gives a solution with a CD of around 1.2. This is close to literature values of a 2D wedge in a flow.

However, when I add the inflation layers (and change nothing else in the mesh), the solution diverges after one timestep and I get a warning that the turbulent viscosity is limited to a viscosity ratio of 1e5 in several thousand cells.
In the end Fluent stops iterating with the message:

The first inflation layer thickness is set such that y+ is around 30. Setting it such that y+ is 1 did not solve the divergence.

I've read up on the viscosity ratio warning in different posts here and in other internet resources, but the remedies (refining the mesh, under-relaxing the k and e) did not work for me.

I'm surprised that adding an inflation layer has such a big (negative) effect on my solution. Can someone explain what is happening here?
Should I just leave the inflation layers out all together (sounds like a bad idea)?

1. Geometry overview, flow comes from the left, normal to the boundary:
https://dl.dropboxusercontent.com/u/390388/geo.png

2. Geometry close-up:
https://dl.dropboxusercontent.com/u/.../geo-close.png

The mesh without inflation layers looks as follows:

3. Mesh overview:
https://dl.dropboxusercontent.com/u/390388/mesh.png

4. Mesh refined area:
https://dl.dropboxusercontent.com/u/...esh-close1.png

5. Mesh around wedge:
https://dl.dropboxusercontent.com/u/...esh-close2.png

And with inflation layers:

6. Mesh around wedge with inflation layers:
https://dl.dropboxusercontent.com/u/.../inflation.png

7. Mesh around wedge nose with inflation layers:
https://dl.dropboxusercontent.com/u/...tion-close.png

Have a look at the cells at the sharp trailing edges of your geometry.
I guess they have very small angles.

The trailing edge looks like this:

https://dl.dropboxusercontent.com/u/390388/te.png

How do I prevent too sharp angles in the mesh?

An easy way could be to refine the mesh in this region (which you should do anyway because the mesh is rather coarse here).

I've refined the mesh at the trailing edge by adding an edge sizing restriction on the edges of the wedge. It now looks like this:

https://dl.dropboxusercontent.com/u/...ion-refine.png

Fluent does converge now. Thank you for your help.