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 L 1544 ; for the thermal and rotational energy ratios with respect to the potential energy , we assume the values \alpha = 0.3 and \beta = 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 .