Appropriate sub-grid scale models for Large-Eddy Simulation of supercritical mixing and combustion are desirable for affordable numerical investigations of high-pressure combustion. Most of the existing numerical schemes, however, generally adopt the models developed for low-pressure conditions without examination of the underlying assumptions, which are not guaranteed to be the case in the context of supercritical mixing and combustion. Two-dimensional Direct Numerical Simulations of a Liquid Oxygen (LOX)/methane flame stabilized by a splitter plate are performed to provide the database for a systematic examination of the underlying model assumptions. The characteristic Reynolds number is 1.5×105. The density ratio ranges from 13.6 to 125. Both cold flow and combustion cases are included. A series of findings are made for supercritical combustion. The uncertainties caused by calculating density from filtered variables overshadow all other SGS terms. The PDF of the mixture fraction deviates from the beta-function distribution at relatively large variance of scalar dissipation. The scalar dissipation is playing a less important role in determining the sub-grid turbulence/chemistry interactions. DNS data extracted PDF method is proposed for the calculation of density, thermodynamic and transport properties, and species concentration. A improved version of flamelet-progress-variable method with DNS extracted PDF for species concentration and reaction rates are proposed for turbulence/chemistry interaction modeling in supercritical combustion.