Sintering is a high temperature process for the consolidation of ceramic, metal and polymer powders. The Discrete Element Method (DEM) has been effectively used to model the sintering process at the particle scale considering spherical particles. However, standard manufacturing processes rarely deal with spherical particles. As sintering is a curvature-controlled process, it is important to take into account the deviation from sphericity. This study presents a DEM sintering model for non-spherical particles. The description and dynamic evolution of arbitrary shape particles is achieved by using the Level Set discrete element method (LS-DEM). The original LS-DEM approach uses boundary nodes on the particles to detect contacts. We employ an optimization-based contact detection approach. This improves the capture of small contacts, which is important for a correct description of sintering evolution with reasonable CPU-time consumption. A Newton-Raphson scheme is employed for the optimization algorithm. The normal force and neck size evolution expressions of spherical particles are adapted for arbitrary shape particles by using the local curvature at the contact. The developed model is validated for elastic contacts on superquadric ellipsoids. It is compared with standard DEM on spheres for sintering. The model is applied to investigate the consolidation kinetics of a packing of ellipsoidal particles. It is shown, that a deviation from sphericity is beneficial for both prolate and oblate ellipsoids. An optimum aspect ratio is evaluated, demonstrating that particles that are too elongated slow down densification kinetics.