DNS simulations are carried out to obtain information in the dense zone of a spray where nearly no experimental data are available. Interface tracking is ensured by Level Set method, Ghost Fluid Method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. Coupling between Level Set and VOF method is used for mass conservation. Fluid motion is predicted with a projection method for incompressible flows. The numerical methods are described and validations are presented. First results are then presented for 3D simulation of the primary break-up of a liquid jet with the Level Set-VOF-Ghost Fluid method and the results can help to determine closure relation in the ELSA model [Part II of the paper] which is based on a single-phase Eulerian model and on the transport equation for the mean liquid/gas interface density in turbulent flows.