Using the two-dimensional MAC scheme, direct numerical simulations wer
e made to examine the double localized traveling wave (DLTW) state in
horizontal layers of binary fluid mixtures heated from below described
by the full hydrodynamic equations. Convection near the saddle-node p
oint develops modulation traveling waves and eventually evolves into D
LTW. The agreement between numerical and experimental results indicate
s the significance of our direct simulation using full hydrodynamic eq
uations.