High pressure liquid propellants are used in many of the modern day rocket combustion engines. Computational analysis of turbulent combustion avoids experimental difficulties that encounter during such experiments. However, some numerical difficulties are still present for solving supercritical combustion regimes. In the present study, several of numerical difficulties have been studied in details and their possible intermittencies are discussed. The computations are performed using ANYSY FLUENT. Numerical simulation of LOx-GH₂ combustion in a shear coaxial injector under supercritical pressure is analysed in 2D domain. Experimental results obtained from MASACOTTE test case are used to validate the numerical model. Different gas models are investigated along with different turbulence interaction models, e.g. Finite rate chemistry, Flamelet bases presumed-PDF model and Eddy dissipation model. RANS calculation is performed using k-ε turbulence model, while the mixing length parameters C_1ε and C_2ε are also modified to correctly predict the behavior of the spreading jet. Finally, the comprehensive assessment has been made amongst the different turbulent chemistry-interaction models, where the kinetics effect is invoked using two different chemical mechanisms.