In this work, we compare the spatial distribution of the plasma parameters along the 1999 June 11 coronal mass ejection (CME)-driven shock front with the results obtained from a CME-like event simulated with the FLIPMHD3D code, based on the FLIP-MHD particle-in-cell method. The observational data are retrieved from the combination of white-light coronagraphic data (for the upstream values) and the application of the RankineHugoniot equations (for the downstream values). The comparison shows a higher compression ratio X and Alfvénic Mach number M A at the shock nose, and a stronger magnetic field deflection d toward the flanks, in agreement with observations. Then, we compare the spatial distribution of M A with the profiles obtained from the solutions of the shock adiabatic equation relating M A , X, and Bn q (the angle between the upstream magnetic field and the shock front normal) for the special cases of parallel and perpendicular shock, and with a semi-empirical expression for a generically oblique shock. The semi-empirical curve approximates the actual values of M A very well, if the effects of a non-negligible shock thickness sh d and plasma-to magnetic pressure ratio u b are taken into account throughout the computation. Moreover, the simulated shock turns out to be supercritical at the nose and sub-critical at the flanks. Finally, we develop a new one-dimensional Lagrangian ideal MHD method based on the GrAALE code, to simulate the ion-electron temperature decoupling due to the shock transit. Two models are used, a simple solar wind model and a variable-γ model. Both produce results in agreement with observations, the second one being capable of introducing the physics responsible for the additional electron heating due to secondary effects (collisions, Alfvén waves, etc.).