A diagnostic investigation regarding the turbulent combustion is analyzed for supersonic co-axial flame. The Mathematical formulation is based on the hybrid RANS/LES formulation for compressible reacting flows. A validation case study is performed for an experimental case with three levels of different grid system with three different high resolution schemes namely 3rd-order MUSCL scheme, a 5th-order WENO scheme and multi-dimensional 5th-order oMLP scheme. The time-averaged results of the experimental case shows the importance of fine grid resolution and high-order accurate numerical scheme for reliable prediction, capturing the fine scale instabilities of the supersonic turbulent combustion. The oMLP scheme exhibits a remarkable performance without a big expense. An analysis of the flow field is carried out to investigate the supersonic turbulent flame structure. The comparison of the combustion parameters including OH mass fraction, scalar dissipation rate and flame index reveals that the supersonic combustion of the validation case has a characteristics of turbulent lifted flame where the combustion is held mostly at premixed mode following turbulence mixing at the shear layer.