Two different numerical simulation codes (the SPLIT/NE code and the Po
liTo code) are examined in this paper by comparing results for non-equ
ilibrium flow cases using two different geometries, a hemisphere-cylin
der-flare (axisymmetric) and a hyperbola-flare-cylinder configuration
(axisymmetric and 2-D plane). The solution methods implemented in the
codes are essentially different (finite difference, bow shock fitting,
matrix splitting and Runge-Kutta high accuracy schemes for SPLIT/NE a
nd finite volume, shock capturing, flux difference splitting and E.N.O
. high accuracy schemes for PoliTo). The flow simulations are done emp
loying physical models of different complexity (inviscid and viscous f
lows, chemically reacting flows in vibrational equilibrium and non-equ
ilibrium, steady and unsteady hows). Comparing the solutions for the d
ifferent codes, a very good agreement is obtained for both the hemisph
ere-cylinder-flare flow and the 2-D plane hyperbola-flare-cylinder flo
w. For relatively small flare angles, this is also true for the axisym
metric hyperbola-flare-cylinder flow; however, for larger flare angles
, differences in the solutions can be detected which can be addressed
to the formation of a strong recirculation bubble behind the detached
flare shock.