Bubble interactions have significant impact on the shape and motion of bubbles, and therefore the dynamics of bubbles in a swarm may be considerably different from that of an isolated bubble. This research presents a numerical study of bubble interactions using a novel lattice Boltzmann method (LBM). By using the adaptive mesh refinement (AMR) and the multiple-relaxation-time (MRT) algorithm, this technique is able to accurately capture the deformation of the interface, and can remain numerically stable for low Morton number and high Reynolds number flows. The numerical approach is briefly illustrated, and validated with the experimental results of the buoyant rise of an isolated bubble in the literature. Then the method is applied to simulate the interaction between multiple bubbles during their buoyant rise. A pair of bubbles with spherical or ellipsoidal shapes is first simulated under different configurations and rise velocities. Both attractive and repulsive interactions are observed in the simulations depending on the relative position and the Reynolds number. When the Reynolds number is sufficiently high, the bubble-wake interaction is found to be the main interaction mechanism, which results in strong attraction between the ellipsoidal bubbles in vertical or oblique arrangement. Simulations for a group of 14 bubbles are also carried out, and effects of the bubble shape and Reynolds number on the spatial distribution of the bubbles are briefly discussed. In general, a good agreement is found between the current simulation and the experimental and numerical results reported in the literature. (C) 2011 Elsevier Ltd. All rights reserved.