  One approach to reduce the cost to simulate transitional compressible
boundary layer flow is to adopt a near body reduced domain with boundary
conditions enforced to be compatible with a computationally cheaper 3D RANS
simulation. In such an approach it is desirable to enforce a consistent
pressure distribution which is not typically the case when using the standard
Riemann inflow boundary condition. We revisit the Riemann problem adopted in
many DG based high fidelity formulations. Through analysis of the 1D linearised
Euler equations it is demonstrated that maintaining entropy compatibility with
the RANS simulation is important for a stable solution. The maintenance of
Riemann invariant at outflow leaves one condition that can be imposed at the
inflow. Therefore the entropy-pressure enforcement is the only stable boundary
condition to enforce a known pressure distribution. We further demonstrate that
all the entropy compatible inflow Riemann boundary conditions are stable
providing the invariant compatible Riemann outflow boundary condition is also
respected. Although the entropy-pressure compatible Riemann inflow boundary
condition is stable from the 1D analysis, 2D tests highlight divergence in the
inviscid problem and neutrally stable wiggles in the velocity fields in viscous
simulations around the stagnation point. A 2D analysis about a non-uniform
baseflow assumption provides insight into this stability issue (ill-posedness)
and motivate the use of a mix of inflow boundary conditions in this region of
the flow. As a validation we apply the proposed boundary conditions to a
reduced domain of a wing section normal to the leading-edge of the CRM-NLF
model taken out of a full 3D RANS simulation at Mach 0.86 and a Reynolds number
of 8.5 million. The results show that the entropy-pressure compatible Riemann
inflow boundary condition leads to a good agreement in pressure distribution.
