© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. We test here the first stage of a route of modifications to be applied to the public GADGET2 code for dynamically identifying accretion centers during the collision process of two adjacent and identical gas cores. Each colliding core has a uniform density profile and rigid body rotation; its mass and size have been chosen to represent the observed core L1544; for the thermal and rotational energy ratios with respect to the potential energy, we assume the values α = 0.3 and β = 0.1, respectively. These values favor the gravitational collapse of the core. We here study cases of both head-on and off-center collisions, in which the pre-collision velocity increases the initial sound speed of the barotropic gas by up to several times. In a simulation the accretion centers are formed by the highest density particles, so we here report their location and properties in order to realize the collision effects on the collapsing and colliding cores. In one of the models, we observe a roughly spherical distribution of accretion centers located at the front wave of the collision. In a forthcoming publication we will apply the full modified GADGET code to study the collision of turbulent cores.