This work aims to achieve numerical simulation of the bouncing of an air bubble immersed in a liquid when it reaches a free surface, as a continuation of experiments made in the Universitat Politècnica de Catalunya by the student Francesc Suñol. The thesis has been carried out with a computer code which has been developed by the INTERFACE group of the Institut de Mécanique des Fluides de Toulouse. This code, called JADIM, does not have any explicit interface reconstruction process, so coalescence happens when two interfaces are close enough. As a consequence, the main part of this thesis is dedicated to the changes that have been introduced in the computer code to make it able to simulate the bouncing without the process ending up in coalescence. These changes include an interface thinning algorithm, a function to track interfaces of both bubble and free surface and to calculate the distance between them, a routine that creates a grid taking into account those measurements, and an interpolator to provide the new nodes with information about their physical properties. Tests of the modified code show independence of most of the parameters with the final results, although there have been problems detected in the values of terminal velocity, which is about 30% higher than expected, and a divergence in the values of the velocity during the velocity inversion preceding the bouncing. The first problem is related to the thinning algorithm, and the second seems to be caused by the thickness of the interfaces, which relies in the size of their cells. A possible solution for these problems could be finishing a second interface thinning algorithm, to test whether the old one actually causes the high terminal velocity, and a modification of the remeshing process to reduce the cell size more gradually when the bubble reaches the surroundings of the free surface.