A novel numerical scheme for unstructured compressible large eddy simulation (LES) is developed. This method is low-dissipative and less sensitive to the quality of the computa-tional grid and is targeted for performing large-scale, high-fidelity simulations of turbulent flows in complex configurations. The objective of this work is to introduce this method, present a rigorous validation study, and demonstrate the application to a variety of jet configurations. This technique is validated by predicting the flow and noise emitted from a single-stream pressure-matched hot supersonic jet. Nearfield ow as well as farfield noise computed using an acoustic projection method is studied and compared to experimental measurements obtained by Dr. James Bridges at NASA Glenn. Mesh refinement studies and sensitivity study on selecting the acoustic projection surface are provided. To test the method's performance in a variety of jet noise configurations, it is applied to a high bypass ratio dual-stream jet at sonic conditions, a vertical supersonic jet impinging on the ground, and a horizontal supersonic jet impinging on an angled jet blast deflector.