The 2D edge plasma transport code EDGE2D-EIRENE has been upgraded to account for the actual material and geometric properties of the newly installed ITER-Like Wall (ILW) at JET. This includes the simulation of beryllium and tungsten impurities as well as a revised treatment of sputtering by main plasma and impurity atoms and ions (including self sputtering). In this work, two L-mode density regimes, a sheath limited and a high recycling regime, are presented with a power scan from 2 to 6MW. Tungsten is self consistently simulated with the Scrape Off Layer (SOL) plasma by the EDGE2D-EIRENE code. A detailed analysis of the tungsten sputtering is presented, resolving the individual contributions of the different atomic and ion species in the simulations.