Liquid jets in crossflow are used in a variety of fuel injection systems. Of particular interest in this work is the injection of liquid fuel into supersonic crossflow at scramjet startup conditions. Due to the short residence times of fuel in the combustor, it is imperative to efficiently and rapidly atomize and mix the fuel. Experiments often have limited ability to observe all of the wide range of scales and complicated liquid structures present in these conditions. Numerical simulations can provide additional insights into these complex flows. In this work, a numerical approach for the solution of compressible multi-component flows with capillary effects is presented along with additions to enable the solution of large computational problems. The approach is then validated against a non-turbulent round jet in subsonic crossflow. Comparisons to jet trajectory, column breakup location, and instability wavelengths are completed. A liquid jet in supersonic crossflow is simulated and the effects of a turbulence in the jet inflow are investigated. The jet trajectory is compared against experimental results. Although differences between the experimental results and numerical simulations are observed, the results suggest jet inflow turbulence can impact the atomization process in supersonic crossflow conditions and quantification of inflow conditions is important.