For the first time, the lattice gas automata method is used to simulate small-scale oceanic fronts of river discharge type. With this method, which is based on statistical physics, round-off errors and computer code instabilities are absent, while mass and momentum conservation are easily implemented. We have developed a quasi-stationary lattice gas automata model which describes the evolution process of such a front. This numerical model reproduces the characteristic convergence of the velocity field from both sides near the frontal interface. Furthermore, the overall Richardson number Rio is verified to be the governing dimensionless parameter. A typical density current is established only for Rio>0.20 and in much shorter time than the total simulation time, which corresponds to the Brunt-V¿is¿l¿ time period. For longer simulation times the front remains stable, but its interface is blurred owing to diffusion. Moreover, the mean mass entrainment is found to be positive for Rio above 0.75, which favors the frontal stability. Our results are, in general, in qualitative and partly in quantitative agreement with observations in the field, tank experiments, and other numerical models. ¿ American Geophysical Union 1993