  We present a numerical study of the flow states and reversals of the
large-scale circulation (LSC) in a two-dimensional circular Rayleigh-B\'enard
cell. Long-time direct numerical simulations are carried out in the Rayleigh
number ($Ra$) range $10^{7} \le Ra \le 10^{8}$ and Prandtl number ($Pr$) range
$2.0 \le Pr \le 20.0$. We found that a new, long-lived, chaotic flow state
exists, in addition to the commonly observed circulation states (the LSC in the
clockwise and counterclockwise directions). The circulation states consist of
one primary roll in the middle and two secondary rolls near the top and bottom
circular walls. The primary roll becomes stronger and larger, while the two
secondary rolls diminish, with increasing $Ra$. Our results suggest that the
reversal of the LSC is accompanied by the secondary rolls growing, breaking the
primary roll and then connecting to form a new primary roll with reversed
direction. We mapped out the phase diagram of the existence of the LSC and the
reversal in the $Ra$-$Pr$ space, which reveals that the flow is in the
circulation states when $Ra$ is large and $Pr$ is small. The reversal of the
LSC can only occur in a limited $Pr$ range. The phase diagram can be understood
in terms of competition between the thermal and viscous diffusions. We also
found that the internal flow states manifested themselves into global
properties such as Nusselt and Reynolds numbers.
