The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a vortex‐in‐cell numerical algorithm. The algorithm is used to simulate the competition among the bubbles that are formed in the interface when the density ratio of the two fluids is very large. Several multifrequency initial conditions and the effect of surface tension have been considered. It is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Phys. D12, 45 (1984)] and with the results obtained by using Zufiria’s [Phys. Fluids31, 440 (1988)] model.