In order to understand supercritical jet flows further, well resolved large eddy simulations (LES) of a n-dodecane jet mixing with surrounding nitrogen are conducted. A real fluid thermodynamic model is used to account for the fuel compressibility and variable thermophysical properties due to the solubility of ambient gas and liquid jet using the cubic Peng-Robinson equation of state (PR-EOS). A molar averaged homogeneous mixing rule is used to calculate the mixing properties. The thermodynamic model is coupled with a pressure-based solver to simulate multispecies reacting flows. The numerical model is based on a second order accurate method implemented in the open source OpenFOAM-6 software. First, to evaluate the present numerical model for sprays, 1D advection and shock tube benchmark problems at supercritical conditions are shown. Second, a cryogenic nitrogen injection with a jet velocity of 4.9 m/s into a supercritical nitrogen environment at 4 MPa and room temperature is considered to carry out a grid resolution study, and the corresponding results are evaluated against experimental data of Mayer et al. Then, to assess the effects of thermophysical property variations due to mixing of two species, a high-pressure jet of n-dodecane at transcritical and supercritical temperatures at 200 m/s into high-pressure and high-temperature nitrogen environment is studied. Detailed analysis of the species dispersion and mixing are presented for various conditions. The present LES simulations of n-dodecane jets show massive shear forces and high hydrodynamic pressure fluctuations caused by the high-speed jet. The predicted results of flow and thermophysical properties are in close agreement with the available literature data.