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For various densities of gas jets including very light hydrogen and relatively heavy ones, the penetration length and diffusion process of a single high-speed gas fuel jet injected into air are computed by performing a large eddy simulation (LES) with fewer arbitrary constants applied for the unsteady three-dimensional compressible Navier-Stokes equation. In contrast, traditional ensemble models such as the Reynolds-averaged Navier-Stokes (RANS) equation have several arbitrary constants for fitting purposes. The cubic-interpolated pseudo-particle (CIP) method is employed for discretizing the nonlinear terms. Computations of single-component nitrogen and hydrogen jets were done under initial conditions of a fuel tank pressure of gas fuel = 10 MPa and back pressure of air = 3.5 MPa, i.e., the pressure level inside the combustion chamber after piston compression in the engine.