A new meshless Lagrangian particle code has been developed to tackle the challenging numerical modeling of primary atomization. In doing so the correct treatment and representation of the interfacial physics are crucial prerequisites. Grid based codes using interface tracking or interface capturing techniques, such as the volume of fluid or level set method, exhibit difficulties regarding mass conservation, curvature capturing and interface diffusion. The objective of this work is to overcome these shortcomings of common state-of-the-art grid based approaches. Our multidimensional meshless particle code is based on the smoothed particle hydrodynamics (SPH) method. Various test cases have been conducted, by which the capability of accurately capturing the physics of single and multiphase flows is verified and the future potential of this approach is demonstrated. Compressible as well as incompresssible fluids can be modeled. Surface tension effects are taken into account by two different models. Solid walls as well as periodic boundary conditions offer a broad variety of numerically modeling technical applications. In a first step, single phase calculations of shear driven liquid flows have been carried out. Furthermore, the disintegration of a gravity driven liquid jet emerging from a generic nozzle has been investigated in free surface simulations. The typical formation of a meniscus due to surface tension is observed. Spray formation is qualitatively in good agreement compared to experiments. Finally, the results of a two-phase simulation with a fluid density ratio of 1000, which is similar to a fuel-air fluid system as in airblast atomizers, are presented. The surface minimization and pressure jump across the droplet interface due to surface tension can be predicted accurately. The test cases conducted so far demonstrate the accuracy of the existing code and underline the promising potential of this new method for successfully predicting primary atomization.