Dear all,

I was trying to run a few cases at a higher Re on PyFR.1.12.1. The first case was a flow over 2d square cylinder at Re=2.2e4 using AC solver. As a start, I initiated the cases with `p=1`

and a sponge field for 50s, dt = 5e-3 and pseudo dt=2e-4. Everything seemed fine except the pressure residual was quite stiff and remained to be about 0.3~0.5. Then I restarted the case for more 50s with `p=2`

and `[solver-dual-time-integrator-multip]`

, the pressure residual dropped down to about 0.1~0.2, but the forces on the square were strange and had no periodicity. Thus, I extended the calculation for another 200s, but in vain. The forces still remains unstable, and the pressure residual was over 0.1. The profile of force-time and the contours of pressure and velocity (t=120s and 240s) are shown below.

t=120s

t=240s

However, It’s very encouraging that every time I reviewed the topics posted on the forum, I was able to capture some new tips.

- The first tip is using the anti-alias, due to the aliasing error that may occur on non-linear problems, it’s advised to adopt
`anti-alias = (flux, surf-flux)`

option to stabilize the result. But once I activated the option, no matter how small dt and pseudo dt I set, the Nan problem appeared in the first period. - The second tip is to refine the mesh and decrease the dt and pseudo dt, I generated a finer mesh (almost 2 times the first mesh and kept the yplus < 3) but still got the same unstable problem even for a long run.
- The third tip is using a higher polynomial order like setting
`p = 3/4`

. But due to the explicit pseudo time stepper and the multi-p method, the cost of calculation was quite high (nearly 100hs), especially for a long run. I know it’s hard to maintain balance between the efficiency and accuracy, but stability, in my opinion, would be supposed to be guaranteed in the first place.

Can someone give me any hints on how to stabilize the case and advice on improving the performance of the calculation? The mesh file and ini file are attached below.

Many thanks, Thatcher.