Dual fuel engines using diesel and fuels that are gaseous at normal conditions are receiving increasing attention. They permit to achieve the same (or better) than diesel power density and efficiency, steady-state, and substantially similar transient performances. They also permit to deliver better than diesel engine-out emissions for CO2, as well as particulate matter, unburned hydrocarbons, and nitrous oxides. The adoption of injection in the liquid phase permits to further improve the power density as well as the fuel conversion efficiency. Here, a model is developed to study a high-pressure, 1600 bar, liquid phase injector for liquefied natural gas (LNG) in a high compression ratio, high boost engine. The engine features two direct injectors per cylinder, one for the diesel and one for the LNG. The engine also uses mechanically assisted turbocharging (super-turbocharging) to improve the steady-state and transient performances of the engine, decoupling the power supply at the turbine from the power demand at the compressor. Results of steady-state simulations show the ability of the engine to deliver top fuel conversion efficiency, above 48%, and high efficiencies, above 40% over the most part of the engine load and speed range. The novelty of this work is the opportunity to use very high pressure (1600 bar) LNG injection in a dual fuel diesel-LNG engine. It is shown that this high pressure permits to increase the flow rate per unit area; thus, permitting smaller and lighter injectors, of faster actuation, for enhanced injector-shaping capabilities. Without fully exploring the many opportunities to shape the heat release rate curve, simulations suggest two-point improvements in fuel conversion efficiency by increasing the injection pressure.