We present three-dimensional simulations of the dynamics of binary neutron star ( BNS ) mergers from the late stage of the inspiral process up to \sim 20 ms after the system has merged , either to form a hyper-massive neutron star ( NS ) or a rotating black hole ( BH ) . We investigate five equal-mass models of total gravitational mass 2.207 , 2.373 , 2.537 , 2.697 and 2.854 M _ { \odot } , respectively ; and four unequal mass models with M _ { \mathrm { ADM } } \simeq 2.53 M _ { \odot } and q \simeq 0.94 , 0.88 , 0.83 , and 0.77 ( where q = M ^ { ( 1 ) } / M ^ { ( 2 ) } is the mass ratio ) . We use a semi-realistic equation of state ( EOS ) , namely the seven-segment piece-wise polytropic SLyPP with a thermal component given by \Gamma _ { th } = 1.8 . We have also compared the resulting dynamics ( for one model ) using both , the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector , and also different reconstruction methods for the matter sector , namely PPM , WENO and MP5 . Our results show agreement and high resolution , but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions . One of the important characteristics of the present investigation is that for the first time , it has been done using only publicly available open source software : the Einstein Toolkit code , deployed for the dynamical evolution ; and the LORENE code , for the generation of the initial models . All of the source code and parameters used for the simulations have been made publicly available . This not only makes it possible to re-run and re-analyze our data , but also enables others to directly build upon this work for future research .