This is the first part of direct numerical simulation (DNS) of double-diffusive
convection in a slim rectangular enclosure with horizontal temperature and concentration
gradients. We consider the case with the thermal Rayleigh number of 10^{5}, the
Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature
being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th-order
upwind compact scheme was developed for approximation of convective terms,
and a three-stage third-order Runge-Kutta method was employed for time advancement.
Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow
of transition is a complex series changing from the steady to periodic, chaotic, periodic,
quasi-periodic, and finally back to periodic. There are two types of periodic flow, one
is simple periodic flow with single fundamental frequency (FF), and the other is complex
periodic flow with multiple FFs. This process is illustrated by using time-velocity
histories, Fourier frequency spectrum analysis and the phase-space trajectories.