The atomization process of turbulent liquid jets is as of this day not well understood. Detailed numerical simulations can help study the fundamental mechanisms in regions where experimental access and analysis is difficult. This paper presents simulation results of the primary atomization of round turbulent liquid jets injected into stagnant high-pressure air under diesel engine conditions using the refined level set grid approach. A balanced force approach is used to accurately account for surface tension forces using an interface projected curvature method to minimize erroneous spurious currents. Broken off, small-scale nearly spherical drops are transferred into a Lagrangian point particle description allowing for full two-way coupling. The physical mechanisms resulting in the initial breakup of the jet are discussed. We analyze the impact of finite grid resolution on the phase interface geometry of the injected liquid core and discuss the impact of the automatic topology-change length scale inherent in the fixed grid interface, capturing methods like the level set method. Drop size distributions resulting from primary atomization are presented, showing that grid-independent drop sizes can be achieved for liquid structures resolved by at least six grid points.