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Numerical analyses of the liquid fuel injection and the subsequent fuel-air mixing in a high-tumble, long-stroke direct injection engine at operation conditions of 2000 RPM are presented. The Navier-Stokes equations are numerically solved with a finite-volume method for compressible flow based on a hierarchical Cartesian mesh. The solid wall boundaries are represented by a conservative multiple cut- and split-cell method, where a semi-Lagrange level-set solver is used to track the location of the individual moving boundaries. To determine the fuel vapor before ignition, a two-way coupled large-eddy simulation of the turbulent flow field with the spray droplets is conducted. Due to the large number of spray droplets, a Lagrangian Particle Tracking (LPT) algorithm is used to predict the liquid spray penetration and evaporation.