We are developing LES capability for the simulation of mixing and combustion of transversely injected fuel jets in hot supersonic crossflows. This paper describes the numerical algorithm being used and its performance on several problems involving shock wave dynamics in different configurations. Also shown are results from preliminary calculations of a transitional transverse jet injected into a supersonic crossflow computed on a coarse mesh. These results are discussed and similarity with the experimental observations are noted. Further developments, such as inclusion of the jet hole geometry, simulation of a turbulent boundary layer upstream of the injector, and higher overall resolution in the jet shear-layers are planned for the future. These would enable detailed comparisons with the available experimental data. The numerical algorithm which is based on an extension of the approach proposed by Cook and Cabot for shock-turbulence interaction is found to be suitable for LES of complex supersonic flows.