We extensively investigate the inertial coalescence process of a water drop merging with another water drop, particularly including a water flat pool, via three-dimensional lattice Boltzmann simulations. After the two drops contact, a narrow liquid bridge is formed, which induces the coalescence process. The growth dynamics of the bridge has been a fundamental issue in coalescence study for a long time. Recently, the X-ray imaging study for the short-time dynamics of water coalescence on a flat water pool reported that asymmetry of drops affects hydrodynamics of coalescence and its neck-growth. In this report, we simulate a water drop coalescence at bottom drops with various sizes containing asymmetric conditions such as a flat water pool. We find that the thickness of the bridge grows quantitatively as the bottom drop size increases up to infinity where its surface is flat. This result shows sub-diffusive behavior with exponent of 2/5, rather than normal diffusion with exponent of 1/2 in the scaling law equation, which has been found in two identical drops. Published by AIP Publishing.