We present a numerical investigation of the coalescence of a drop with a pool of the same liquid. The simulations were carried out with both viscous Newtonian and viscoelastic fluids based on an axisymmetric high density ratio lattice Boltzmann method with a diffuse interface coupled with the Oldroyd-B Model. Particular attention was paid to the widening dynamics of the liquid bridge between the drop and the pool and to the velocity fields within both the drop and liquid bulk. The results were compared with experimental data obtained using a high-speed camera and a micro-particle image velocimetry (μ-PIV) and displayed satisfactory agreement. In particular, the simulated temporary evolution of the rescaled coalescing width of the liquid bridge as a function of the normalized time compares favorably with the experimental results for both the inertially limited viscous and the inertial regimes for short and long time.