  Modern high-order discretizations bear considerable potential for the
exascale era due to their high fidelity and the high, local computational load
that allows for computational efficiency in massively parallel simulations. To
this end, the discontinuous Galerkin (DG) framework FLEXI was selected to
demonstrate exascale readiness within the Center of Excellence for Exascale CFD
(CEEC) by simulating shock buffet on a three-dimensional wing segment at
transsonic flight conditions. This paper summarizes the recent progress made to
enable the simulation of this challenging exascale problem. For this, it is
first demonstrated that FLEXI scales excellently to over 500 000 CPU cores on
HAWK at the HLRS. To tackle the considerable resolution requirements near the
wall, a novel wall model is proposed that takes compressibility effects into
account and yields decent results for the simulation of a NACA 64A-110 airfoil.
To address the shocks in the domain, a finite-volume-based shock capturing
method was implemented in FLEXI, which is validated here using the simulation
of a linear compressor cascade at supersonic flow conditions, where the method
is demonstrated to yield efficient, robust and accurate results. Lastly, we
present the TensorFlow-Fortran-Binding (TFFB) as an easy-to-use library to
deploy trained machine learning models in Fortran solvers such as FLEXI.
