The study focuses on high-fidelity numerical simulations of several operating modes of the HIFiRE 2 Direct Connect Rig (HDCR) facility experiment. Wall Modeled Large Eddy Simulations of supersonic combustion have been performed in order to analyze the main flow features and compare wall pressure distributions with the experimental data. The combustion model is based upon finite-rate chemistry, with the Arrhenius-based closure provided by an ethylene-air skeletal reaction mechanism. A monotonicity-preserving flux reconstruction scheme based on central differencing and flux limiters was implemented in the solver, which has been written using the open-source CFD toolbox OpenFOAM. The governing equations were discretized and solved on a hexahedral structured grid, using explicit time integration and parallel computing.