  Liquid lens coalescence is an important mechanism involved in many industrial
and scientific applications. It has been investigated both theoretically and
experimentally, yet it is numerically very challenging to obtain consistent
results over the wide ranges of surface tension and viscosity values that are
necessary to capture the asymptotic temporal behavior in the viscous and
inertial limits. We report results of massively parallel simulations based on
the color gradient lattice Boltzmann method, which overcome these limitations,
and investigate the scaling laws of both regimes. For the two-dimensional case
we find good agreement with the similarity solution of the thin-sheet equation,
where in the viscous regime the connecting bridge grows linearly with time and
in the inertial regime proportionally to $t^{2/3}$. In three dimensions, the
viscous growth of the bridge also exhibits a linear time dependence, while in
the inertial regime the growth of both the bridge height and the bridge width
is proportional to $t^{1/2}$.
