  A high-order flux reconstruction solver has been developed and validated to
perform implicit large-eddy simulations of industrially representative
turbomachinery flows. The T106c low-pressure turbine and VKI LS89 high-pressure
turbine cases are studied. The solver uses the Rusanov Riemann solver to
compute the inviscid fluxes on the wall boundaries, and HLLC or Roe to evaluate
inviscid fluxes for internal faces. The impact of Riemann solvers is
demonstrated in terms of accuracy and non-linear stability for turbomachinery
flows. It is found that HLLC is more robust than Roe, but both Riemann solvers
produce very similar results if stable solutions can be obtained. For
non-linear stabilization, a local modal filter, which combines a smooth
indicator and a modal filter, is used to stabilize the solution. This approach
requires a tuning parameter for the smoothness criterion. Detailed analysis has
been provided to guide the selection of a suitable value for different spatial
orders of accuracy. This local-modal filter is also compared with the recent
positivity-preserving entropy filter in terms of accuracy and stability for the
LS89 turbine case. The entropy filter could stabilize the computation but is
more dissipative than the local modal filter. Regarding the spanwise spacing of
the grid, the case of the LS89 turbine shows that a $z^+$ of approximately $45
- 60$ is suitable for obtaining a satisfactory prediction of the heat transfer
coefficient of the mean flow. This would allow for a coarse grid spacing in the
spanwise direction and a cost-effective ILES aerothermal simulation for
turbomachinery flows.
